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SACHS
Physics 20 Assignments and Labs
Math Skills
1. How many significant digits are in the following?
a. 7.03 m
b. 0.075 m
c. 6.00 m
d. 200 m
e. 4.2 x 102 m
2. Write the following in scientific notation.
a. 0.00340 m to 3 significant digits (SD) b. 700 m to 2 SD
c. 559 m to 2 SD d. 4.04 m to 2 SD
3. Rounding to correct significant digits.
a. 70.0 m + 2.32 m
b. 552 m + 7.1 m
c. 460 m - 29.8 m d. 75 m x 0.82 m
e. 9.63 m x 1.9 m
f. 6.20 x 102 m x 20.0 m
4. Convert the following and show the appropriate work.
a. 50 km/h --> m/min (8.3 x 102 m/min)
f. 9.81 m/s2 --> cm/min2 (3.53 x 106 cm/min2)
b. 12.1 m/min --> km/h (7.26 x 10-1 km/h)
g. 4.49 m/s2 --> km/h2 (5.82 x 104 km/h2)
2
2
5
2
c. 11.0 m/s --> km/h (1.43 x 10 km/h )
h. 1.20 x 105 km/h-> m/min (2.00 x 106 m/min)
2
2
d. 2.3 x 10 m/s --> km/h (8.3 x 10 km/h)
i. 25.00 cm/min --> m/s (4.167 x 10-3 m/s)
8
9
e. 3.00 x 10 m/s --> km/h (1.08 x 10 km/h)
j. 20 km/(h•s) --> m/s2 (5.6 m/s2)
Velocity, Distance, Time Exercises
1. A car travels at a constant velocity of 13.0 m/s for 21.0 s. Calculate the distance covered during this interval.
(273 m)
2. After firing, a bullet travels at a constant velocity of 1166 km/h. How many meters did it travel in the 5.42 s
before it hit the ground? (1.76x103 m)
3. A cheetah is the fastest land animal over short distances. It can maintain a constant velocity of about 90 km/h
for 8.0 s. What distance can be covered in this time? (2.0x102 m)
4. The police department uses a cruiser that can travel 1734 m at a constant velocity. It covers this distance in
0.0265 h. What is the average velocity that the cruiser is travelling at? (65.4 km/h)
5. The International Space Station (ISS) completes one orbit every 92 minutes and 50 seconds. It travels at 7,707
m/s. How far does it travel in this time? How far above Earth does it orbit? (4.29 x 107 m, 6.83x106m)
6. A dog is chasing a cat. The cat runs in a straight line. The cat runs slowly for 34.0 s at 1.2 m/s and later, as
the dog nears, it runs at an average velocity of 7.6 m/s for 12 s. Calculate the average velocity of the cat for
the whole trip. (2.9 m/s)
7. Farmer Brown wants to travel from Edmonton to Calgary. He drives his truck at 80.0 km/h for 93.0 min. He
stops to drink coffee. This takes him 18.0 min. He then drives his truck at a constant velocity of 115 km/h for
1.20 h. Determine the average velocity that farmer Brown could have driven his truck at to get to Calgary at
the same time had he not stopped for coffee. (85.9 km/h)
8. You ride your bike to school, a distance of 2, 650 m in a time of 12.0 minutes. If you could drive in a
perfectly straight line to school it would be a distance of 1, 430 m, [W]. Calculate your average speed and
velocity. (3.68 m/s, 1.99 m/s [E])
Graphing
1. Identify the independent and dependent variable. The independent (manipulated) variable is the one that the
experimenter is changing (it is what you do). The dependent (responding) variable changes with respect to the
manipulated variable. The independent variable is always graphed on the horizontal (x) axis unless otherwise
stated.
2. Make the graph big (at least one half of the page) and squarish (axes of about even length).
3. The intervals along the x axis must be equal (ex: 1 square = 2 units). The intervals along the y axis must also be
equal (ex: 1 square = 3 units).
4. Labels must be present: Title, label on each axis (including units).
5. Plot the points.
a) If the points seem to be in a straight line (linear), draw a line of best fit.
b) If the points seem to follow a curve, draw a smooth line through the points.
Always use only pencil to draw the graph.
Physics 20
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2 1. During a science demo, an instructor placed a 1.00 kg mass on a horizontal table that was nearly frictionless. The
instructor then applied various horizontal forces to the mass and measured the rate at which the mass was
accelerated for each force applied. The following data was collected.
Force (N)
Acceleration (m/s2)
a) Plot the values given in the table to the left and
5.0
9.8
draw the curve that best fits all the points. (3)
10.0
20.1
b) What is the relationship between the force applied
15.0
29.9
and the acceleration? direct/indirect (1)
20.0
41.2
c) Calculate the slope of your line. (2)
25.0
50.8
d) Write the equation of the line. (2)
e) What would the acceleration be if a 17.8 N force
was applied? (Show two ways to determine this.)
(2)
Total : 10 marks
2. During an experiment, a student measured the mass of 10.0 ml of water. The student then measured the mass of
20.0 ml of water. In this way, the following data was collected.
Volume (ml)
Mass (g)
a) Plot the values given in the table above and draw
10.0
25.0
the curve that best fits all the points. (3)
20.0
35.6
b) What is the relationship between the volume of the
30.0
44.8
water and the mass? (1)
40.0
55.2
c) Calculate the slope of your line. (2)
50.0
65.3
d) Write the equation of the line. (2)
e) What volume is required to obtain a mass of 98.7 g
of water? (1)
f) What does the y intercept represent in this situation?
(1)
Total: 10 marks
3. During an experiment, a student measured the length of a spring as she placed different masses at one end. She
obtained the following table.
Mass(g) Length (cm)
5.32
23.8
6.70
28.4
8.72
34.4
10.96 42.1
12.7 47.0
Physics 20
a)
b)
c)
d)
e)
Plot the values given in the table and draw a line that best fits the points.
Calculate the slope of your line. (2)
Write the equation for your line. (2)
What does the y-intercept represent? (1)
What length would the spring be if a 23.5 g mass was placed at the end?
Total: 9 marks
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3 Chapter 2: Vectors and Projectiles
GRAPHICAL ADDITION OF VECTORS
1. An airplane is flying at 150 m/s in a direction of 60˚ N of W in an air mass moving at 50 m/s in a direction of
40˚ S of W. What is the resulting velocity of the airplane? (150 m/s at 49˚ W of N)
2. A boat is moving at 4.0 m/s in the direction of 75˚ S of W on a river having a current of 3.0 m/s in the
direction of 60˚ E of N. What is the resulting velocity of the boat? (2.8 m/s at 33˚ E of S)
3. What is the resultant force on an object if a 20 N force on it acts 40˚ W of N and a 25 N force acts 30˚ W of
S? (26 N at 14˚ S of W)
Physics 20
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4 Mathematical Addition of VECTORS
1. Tigger Sticks, Wetaskiwin's answer to golf, two putted a green by hitting his ball 3.00 m due North followed
by 5.00 m due West. What would have been the shortest distance to the hole? (5.83 m)
2. A bright young quarterback, Neon Green, ran 8.0 m in a direction of 70˚ N of W on a quarterback sneak.
a) How far North did this take him? (7.5 m)
b) How far West did this take him? (2.7 m)
3. Igor had two golf shots, 100 m at 30.0˚ N of E and 70.0 m North.
a) What total distance was the ball hit towards the East? (86.6 m)
b) What total distance was the ball hit towards the North? (120 m)
4. An airplane flies 200 km at 50.0˚ S of W, then 250 km at 10.0˚ W of S. Find its displacement.
(435 km at 23.3˚ W of S)
5. A Russian student launches the Famous Fiseekski 20 rocket from a classroom in Moscow. After blasting
through the roof, the rocket travels 500 km at 10˚ N of E and then 200 km at 20.0˚ E of N before destroying a
local vodka distillery. Determine the rocket's displacement.
(624 km, 6.2 x 102 km at 64˚ E of N)
6. Reggie hits a ball into right field in Yankee Stadium and runs 90 m East to first base and then 90 m on a
bearing of
55˚ E of N to 2nd base. Calculate Reggie's net displacement. (1.7 x 102 m at 17˚ N of E)
7. A man walks 50.0 m North, 65.0 m at 45.0˚ N of E and finally 40.0 m at 75.0˚ N of E. Calculate his resultant
displacement. (146 m at 22.7˚ E of N)
Projectile Motion
1. A rifle is fired straight up into the air. The initial velocity of the shell is 700 m/s.
a. How long is the shell in the air? (143 s)
b. What is the shell’s maximum height reached? (2.50 x 104m)
2. A cannon is fired at an angle of 60.0˚ from the horizontal. The shell has a velocity of 50.0 m/s when it leaves
the barrel.
a. What is the shell’s initial vertical velocity? (43.3 m/s)
b. How long does it take the shell to reach its maximum height? (4.41 s)
c. How long is the shell in the air? (8.82 s)
d. What is the shell’s horizontal velocity? ( 25.0 m/s)
e. How far from the cannon does the shell land? ( 221 m)
f. What is the shell’s vertical velocity when it hits the ground? (-43.3 m/s)
g. What is the shell’s total final velocity, including angle? (-50.0 m/s at 60˚)
3. A volleyball is served with an initial velocity of 40.0 m/s at an angle of 32.0˚ with the horizontal.
a. How long is the ball in the air? (4.32 s)
b. What is it’s maximum height attained? (22.9 m)
c. How far does the ball travel before hitting the ground? (146 m)
4. A quarter is to be tossed into a glass at the exhibition. The glass is 2.30 m from the person’s hand. If the hand
is at the same level as the top of the glass and the quarter is tossed at an angle of 30.0˚ to the horizontal, what
initial velocity is required to land the quarter in the glass? The coin is in the air for 0.510 s. (5.21 m/s)
5. An arrow is fired from a cliff that is 20.0 m high. The initial velocity of the arrow is 90.0 m/s and it is fired at
an angle of 50.0˚ to the horizontal.
a. How high from the top of the cliff does the arrow reach? ( 242 m)
b. How high from the ground level? (262 m)
c. How long does it take the arrow to reach its maximum height? (7.03 s)
d. How long will it take to fall from its maximum height to the ground level? (7.32s)
e. How far from the cliff will the arrow land? (831 m)
6. A cannon is fired from the top of a fort wall that is 10.0 m high. The cannon ball has a muzzle velocity of 120
m/s and is aimed at an angle of 25˚ to the horizontal. What is the cannon’s range? (1.14 x 103 m)
Physics 20
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5 Chapter 3 Dynamics
Frictional Forces
1. A 2.0 kg cart is a free-body along a frictionless surface. It is accelerated at 0.80 m/s2. What is the force
causing the acceleration? (1.6 N)
2. A 3.5 kg cart has its friction balanced out by sloping the surface on which it sits. What will be the acceleration
when pulled forward by a force of 0.60 N? (0.17 m/s2)
3. A 3.0 kg cart on a level surface slows down at 0.15 m/s2. What is the frictional force decelerating the cart?
(0.45 N)
4. The combined mass of you and a skateboard is 50.0 kg. If someone pulls you with a force of 40 N and if the
force of friction is 28 N what acceleration will occur? (0.24 m/s2)
5. The combined mass of you and a skateboard is 50.0 kg. Someone pulls the skateboard so that it accelerates at
2.00 m/s2. If the frictional force between the skateboard and the road is known to be 30.0 N, what is the
pulling force? (130 N)
6. A 45 000 kg rocket in space fires its engines for 60.0 s. The thrust of the engines is 200000N.
a. What is the acceleration of the rocket? (4.44 m/s2)
b. What is the final speed of the rocket if the initial speed of the rocket was 830 m/s?
(1.10 x 103
m/s)
7. A 450 000 kg space platform must be brought from a speed of 7200 m/s to 7500 m/s. It will do this by firing a
booster rocket with a thrust of 100 000 N. For how many seconds must the rocket burn in order to achieve this
speed increase? (1350 s)
8. A 2.0 kg cart traveling at 1.2 m/s comes to rest in 8.0 s. What is the frictional force acting on the cart? (-0.30
N)
9. When a 2000 kg Buick traveling at 28 m/s has its brakes locked up it will skid to a stop in 4.2s. What is the
force of friction between the road and the car? (-1.3 x 104 N)
10. How much force must be applied by the driving wheels of a 2500 kg car to give it an acceleration of 2.00 m/s2,
if the forces of friction and air resistance together are 600 N? (5.60 x 103 N)
Coefficient of Friction
11. A force of 4.00 N is required to pull a block across a level surface at a steady rate. The force pressing the
surfaces together is 20.0 N. What is the coefficient of friction? (0.200)
12. A lab cart is pushed and allowed to roll freely. The acceleration of the 3.0 kg cart on a level floor is -0.25 m/s2.
The normal force between the floor and the cart is 25 N. What is the coefficient of friction between the cart
and the surface? (0.030)
13. A 4500 kg tool shed on skids requires a force of 25 kN to move it along level ground at a steady speed. What
is the coefficient of sliding friction between the skids and the ground? (0.57)
14. A laboratory cart is known to have a coefficient of friction of 0.0400. It has an unknown load on it. A 6.80 N
force is required to pull it at a steady speed across the table. What is the combined mass of the cart and load?
(17.3 kg)
15. A 2000 kg cart traveling at 20.0 m/s slides to a stop over a distance of 200 m on a snowy road. What is the
coefficient of friction between the cars tires and the road? (0.102)
16. A horizontal force of 2.0 N is applied to a 1.5 kg cart on a horizontal surface. The coefficient of friction is
0.55. What is the acceleration of the cart given that the cart was originally moving? (-4.1 m/s2)
17. What force must be applied to a 2000 kg car on a level road to give it an acceleration 1.00 m/s2 if the
coefficient of friction of its wheels is 0.0800? (3.57 x 103 N)
18. Mr. Zs 2400 kg Buick runs out of gas while travelling at 30.0 m/s along a level road. The coefficient of friction
between the car and the road is 0.0550. What will be the:
a. car’s acceleration? (-0.540 m/s2)
b. distance travelled before coming to rest? (833 m)
Vertical Forces
1. The engine of a 50.0 kg rocket malfunctions shortly after launch. Its thrust is reduced to 250 N. What will be
the acceleration of the rocket? (-4.81 m/s2)
2. A 500 kg rocket sits on a launch pad.
a. What is the force of support that the launch pad exerts on the rocket? (4.91 x 103 N)
b. When the rockets are fired with a thrust of 12.0 kN, what will be the net force on the rocket? (7.10 x
103 N)
c. What will be the acceleration when the rocket thrust is 12.0 kN? (14.2 m/s2)
Physics 20
Assignment and Labs
Page
6 3. Suppose you hang a 1.00 kg mass on a short string that is attached to the bottom of a force scale.
a. What is the force on the string? (9.81 N)
b. If you were to pull upward on the scale so that the force becomes 13.0 N, what will be the acceleration
of the mass? (3.19 m/s2)
c. If you allow the mass to accelerate downward at 4.00 m/s2, what will be the force on the string?
(5.81 N)
4. A newton scale is attached to the ceiling of an elevator. An 80.0 kg person is attached to the bottom of the
scale. What is the reading on the scale when the elevator is
a. at rest? (785 N)
b. rising with an acceleration of 2.00 m/s2? (945 N)
c. coming down with an acceleration of 3.00 m/s2? (545 N)
d. moving upwards between floors at a constant rate of 8.00 m/s? (785 N)
e. If the person notices that the maximum upwards force on the scale is 1050 N. What is the maximum
upward acceleration of this elevator? (3.31 m/s2)
f. If the person notices that the minimum force on the scale is 680 N while descending, what is the
maximum downward acceleration of the elevator? (1.31 m/s2)
5. On a newly discovered planet a 10.0 kg mass falls 12.0 m in 5.60 s. What is the
a. average speed of the fall? (2.14 m/s)
b. final speed of the fall? (4.28 m/s)
c. acceleration of the mass during the fall? (0.764 m/s2)
d. force of gravity on the mass? (7.64 N)
6. A model rocket of mass 0.600 kg is launched by a rocket motor having a thrust of 20.0 N.
a. What is the force of gravity on this rocket? (5.89 N)
b. What will be the net force on the rocket while the motor is firing? (14.1 N)
c. What will be the upward acceleration of the rocket? (23.5 m/s2)
Single Pulley Systems
1. Find the acceleration in the system. M1 = 70.0 kg and M2 = 35.0 kg.
M 1
M 2
(3.27 m/s2 )
2. What is the acceleration of the system given that M1 = 100 kg and M2 = 70.0 kg?
M 1
M 2
(1.73 m/s2 )
3. Determine the acceleration of the 100 kg mass if there is a 15.0 N force due to friction between the 100 kg block
and the table. M1 = 100 kg and M2 = 50.0 kg.
M 1
M 2
(3.17 m/s2 )
Physics 20
Assignment and Labs
Page
7 4. Calculate the acceleration of the following system if the pulley has 10.0 N of frictional force. M1 = 20.0 kg and
M2 = 1.00 kg.
M 1
M 2
(0 m/s2 )
5. Determine the acceleration of the lighter mass if there is a force due to friction of 5.50 N and M1=11.0 kg and
M 1
M 2
M2=12.0 kg.
(0.187 m/s2 up)
6. Determine the acceleration of the 10.0 N overhanging weight if there is a force due to friction of 9.00 N and the
M 1
M 2
(0.327 m/s2)
weight on the table is 20.00 N.
Inclined Planes
1. A 10 kg block of ice slides down a ramp 25 m long, inclined at 10˚ to the horizontal. Calculate
a. the acceleration of the block if the ramp is frictionless (1.7 m/s2)
b. the acceleration of the block if the there is a 0.100 coefficient due to friction (0.73 m/s2)
c. the time that it will take the block to reach the bottom of the ramp if it started from the top of the ramp
at rest and there is a 0.100 coefficient due to friction. (8.23 s)
2. A 63.5 kg skier has just begun descending a 15˚ slope. Assuming that the coefficient due to friction is 0.18,
calculate
a. the acceleration of the skier (0.83 m/s2)
b. her velocity after 7.6 s if she started from rest (6.3 m/s)
3. Barbara is dragging a 24.0 kg log up a hill. The hill makes a 26.0˚ angle with the horizontal. With what force
must she pull in order for the log to accelerate at 2.00 m/s2 towards the top of the hill? (151 N)
4. Candace is pulling a 150 kg tuna fish down a metal ramp with an applied force of 230 N. The ramp is angled at
23.0˚ to the horizontal. There is a 0.300 coefficient of friction. Calculate the
a. acceleration of the fish (2.66 m/s2 , downhill)
b. speed of the fish after 3.00 s if it had an initial speed of 1.50 m/s towards top of hill (6.47 m/s,
downhill)
c. distance that the tuna would travel after 12.0 s (178 m , downhill)
Forces Review
1. If the coefficient of friction is 0.30, how much horizontal force is needed to pull a mass of 15 kg across a level
board at a uniform velocity? (44N)
2. A cart with a mass of 2.0 kg is pulled across a level desk by a horizontal force of 4.0 N. If the coefficient of
kinetic friction is 0.12, what is the acceleration of the cart? (0.83 m/s2)
3. A girl pushed a light snow shovel at a uniform velocity across a sidewalk. If the handle of the shovel is
inclined at 55˚ to the horizontal and she pushes with a force of 100 N along the handle.
a. What is the force of friction? (57 N)
b. What is the coefficient of kinetic friction? (0.70 )
4. A 10 kg block of ice, initially at rest, slides down a ramp 20 m long, inclined at 10˚ to the horizontal.
a. If the ramp is frictionless, what is the acceleration of the block of ice? (1.7 m/s2 )
b. If the µ = 0.10, how long will it take the block of ice to slide down the ramp? (7.4s)
Physics 20
Assignment and Labs
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8 5. A skier has just begun descending a 20˚ slope. Assuming that µ = 0.10, calculate:
a. the acceleration of the skier. (2.4 m/s2)
b. his final velocity after 8.0 s. (19 m/s)
6. A 5.0 kg mass rests on a level frictionless table, attached to a 3.0 kg mass by a light string that passes over a
frictionless pulley. Calculate the acceleration of the two masses. (3.7 m/s2)
7. A 40 kg mass rests on a level frictionless table, attached to a 15 kg mass by a light string that passes over a
frictionless pulley. Calculate the acceleration of the 15 kg mass when it is released. (2.7m/s2)
8. A 3.0 kg mass is attached to a 5.0 kg mass by a strong rope that passes over a frictionless pulley. What will
the acceleration of the system be when the masses are allowed to freely move? (2.5 m/s2)
9. A passenger in an elevator has a mass of 100 kg. Calculate the force exerted on the passenger by the elevator
if the elevator is:
a. at rest. (981 N up)
b. moving upward with an acceleration of 30 cm/s2. (1011 N up)
c. accelerating downward at 0.15 m/s2 (966 N up)
d. moving upward with an uniform velocity of 0.15 m/s. (981 N up)
e. falling freely. (0 N)
10. An elevator and load have a mass of 2000 kg. Calculate the tension in the cable when the elevator is:
a. at rest. (1.96 x 104 N)
b. moving upward at a constant velocity. (1.96 x 104 N)
c. accelerating downward at 1.00 m/s2. (1.76 x 104 N)
d. accelerating upward at 1.00 m/s2. (2.16 x 104 N)
11. A person measures the acceleration of an elevator by hanging a mass from a scale attached to the roof. The
scale reads 98 N when the elevator is at rest and 93 N when moving. What is the acceleration of the elevator?
(-0.50 m/s2)
12. A boy pushing a 20 kg lawn mower exerts a force of 100 N along the handle which is elevated at 37˚ to the
horizontal. Determine:
a. the force that pushed the mower forward. (80 N)
b. acceleration of the lawn mower if the force of friction is 60 N. (1.0 m/s2)
c. the applied force that pushed the mower toward the ground. (60 N)
d. gravitational force exerted on the mower. (2.0 x 102N)
e. total downward force of the mower on the ground when pushed. (2.6 x 102N)
f. normal force the ground exerts on the mower. (2.6 x 102N)
g. effective coefficient of friction. (0.23)
13. An 80 kg person is standing in an elevator on a spring scale calibrated in Newtons. Suppose the elevator
accelerates downward at 3.0 m/s2. What will be the reading on the scale? (544 N)
14. An elevator has a mass of 2.7 x 103 kg. It is pulled up by a cable at an acceleration of 1.2 m/s2. What is the
tension in the cable? (3.0 x 104 N)
15. What would the tension in the cable be if the elevator accelerated down at 1.2 m/s2? (2.3 x 104 N)
16. A fish hangs from a spring scale on the ceiling in an elevator. When the upward acceleration is 1.2 m/s2 the
scale reads 200 N.
a. What is the mass of the fish? (18 kg)
b. When would the scale read 150 N? (1.5 m/s2, down)
c. What would the scale read if the elevator cable breaks? (0 N)
17. A 70 kg skater coasts along ice with a coefficient of friction of 0.010.
a. What is the force of friction? (6.9 N)
b. How long will it take the skater to come to a stop if he/she is initially traveling at 1.0 m/s? (10 s)
18. A 10 kg box is slid across a level floor. The box slides a distance of 6.0 m, stopping in 2.2 s. What is the
coefficient of friction? (0.26)
19. A person pushes a 50.0 kg crate up a ramp that is inclined at 25.0˚ to the horizontal. µ = 0.300 Calculate:
a. Ff (133 N)
b. The force required to keep the crate moving at a constant velocity. (340 N)
Physics 20
Assignment and Labs
Page
9 20. For each of the systems below draw a free body diagram showing all the forces and calculate the acceleration
of the masses. All surfaces and pulleys are frictionless.
a)
4.0 kg
b)
c)
1.0
kg
200 g
100
g
200 g
2.0
kg
3.2 kg
(2.0 m/s2)
(2.3 m/s2)
(2.0 m/s2)
21. Two masses are connected as illustrated. The pulley is frictionless but the surface has a coefficient of friction
of 0.18.
a. What is the acceleration of the system? (2.8 m/s2)
b. For what values of µ will the system not move? (≥ 0.64)
5.0 kg
3.2
kg
22. What is the acceleration of the system illustrated if µ = 0.20?
3.0 kg
30˚
3.0 kg
(1.6 m/s2)
Apparent Weight (extra questions)
2
1. A 4500 kg helicopter accelerates upward at 2.0 m/s . What is the apparent weight of a 70 kg pilot in this
helicopter? (827N)
2. The maximum force (apparent weight) that a grocery sack can withstand, without ripping, is 250 N. If 20 kg
of groceries are lifted from the floor to the table with an acceleration of 5.00 m/s2, will the sack hold? (no)
th
3. A student stands on a Newton scale in an elevator at rest on the 64 floor of a building. The scale reads 836 N.
As the elevator moves up, the scale reading changes to 935 N, then decreases back to 836 N.
2
a. Find the acceleration of the elevator. (1.2 m/s )
th
b. As the elevator approaches the 74 floor, the scale reading drops as low as 782 N. Calculate the
acceleration of the elevator. (-0.63 m/s2)
c. Describe all of the changes in the scale readings you would expect on the ride back to the ground
floor and support your description with physics explanations.
Physics 20
Assignment and Labs
Page
10 The maximum tension in a 2.1 x 10-4 kg spider’s thin strand is 2.0 x 10-3 N. What is the maximum
acceleration of the spider as it ascends the strand? (0.68 m/s2)
3
3
5. A rocket of mass 1.0 x 10 kg is fired to a height of 5.0 x 10 m. The rocket engine shuts off when the rocket
3
reaches a height of 1.0 10 m, and the rocket coasts up to 5.0 x 103 m.
a. Draw a free-body diagram to show the forces acting on the rocket.
i. While the engine is on.
ii. After the engine shuts off.
b. What velocity must the rocket have at the 1.0 x 103m point to enable it to reach 5.0 x 103m? (2.8 x 102
m/s)
c. What acceleration did the rocket experience while the engine was on? Off? (39 m/s2, 9.8 m/s2)
d. What force did the rocket engine exert on the rocket? (4.9 x 104 N)
2
6. An 80 kg person is standing on a Newton scale in an elevator. The elevator accelerates at 3.0 m/s downward.
2
What is the apparent weight of the person? (5.4 x 10 N)
3
2
7. An empty elevator of mass 2.7 x 10 kg is pulled upward by a cable at an acceleration of 1.2 m/s .
4
a. What is the tension in the cable? (3.0 x 10 N)
4
b. What would the tension in the cable be if it were acceleration downward at the same rate? (2.3 x 10
N)
4.
Chapter 4: Gravitational Forces and Fields
Gravitational attraction
2. The radius of the Earth is about 6370 km. A 720 kg spacecraft travels away from the Earth. What would be
the weight (Fg) of the spacecraft at these distances from the Earths surface?
a) 6370 km (1.77 x 103 N) b) 12 740 km (785 N) c) 19 110 km (441 N) d) 32 000 km (195 N)
-11
3. Two 1.00 kg masses are 1.00 m apart. What is the force of attraction between them? (6.67 x 10 N)
5
4. Two locomotives stand so that their centers are 20 m apart. Each has a 1.96 x 10 kg mass. What is the
gravitational force between the two locomotives? (6.4 x 10-3 N)
Use the following information to compute the gravitational force that the sun exerts on Jupiter.
Mass of the Sun = 3.30 x 105 times the mass of the Earth.
Mass of Jupiter = 3.00 x 102 times the mass of the Earth.
Distance between Jupiter and the Sun = 7.80 x 1011 m. (3.88 x 1023 N)
6. The force of attraction between m1 and m2 is 26 N. What will the force become if m2 is tripled and the
distance between it and m1 is halved? (312 N)
7. The force of gravity between A and B is 100 N. When the mass of B is doubled and the distance between it
and A is halved, what is the new force? (800 N)
Gravitational Fields
1. A neutron star is a very compact star having a mass comparable to the sun but a radius only a few kilometers.
a. If you have a mass of 75.0 kg determine your weight on the surface of a neutron star of mass
2.22 x 1030 kg and a radius of 10.00 km. (1.11 x 1014 N)
12
2
b. What is the acceleration of gravity on the surface of this neutron star? (1.48 x 10 m/s )
2. How far above the surface of the earth should you go to find the force of gravity one ninth of what it is on
earth?
(1.27 x 107 m)
3. What is the gravitational field strength on the surface of Venus given that its radius is 6.073 x 106 m and its
mass is 4.88 x 1024 kg? (8.825 m/s2)
4. Calculate the acceleration due to gravity on a 2.00 kg bone if the bone is at an altitude of 150 km above Pluto.
Mass of Pluto 1.20 x 1022 kg. Radius of Pluto 1.15 x 106 m. (4.74 x 10-1 m/s2)
5. What must be the acceleration due to gravity at a certain altitude above the Earth given that a 3.00 kg can of
soup has a weight of 17.87 N? (5.96 m/s2)
6. What would be the weight of a space monkey having a mass of 32.00 kg given that it is placed at an altitude of
4000 km above the Earth's surface? (119 N)
5.
Physics 20
Assignment and Labs
Page
11 Chapter 5 Circular Motion
1. What speed should the rim of a 45 m diameter space station travel so that its inhabitants experience an
acceleration of 10 m/s2. (v = 15 m/s)
2. A rock is attached to a cord and whirled around. If the length of the cord is halved and the rock whirled at the
same speed as before, how will the tension in the cord compare with the former tension? (double)
3. A 3.00 m piece of rope can handle a 100 N force. A 1.50 kg mass is fixed to one end of the cord and whirled
around. Calculate the maximum speed at which the mass can travel without breaking the cord. (14.1m/s)
4. Determine the centripetal force required to prevent a 1200 kg sports car, traveling with a speed of 35.0 m/s,
from skidding when rounding a level curve of radius 120 m. (1.23 x 104 N)
5. A civil engineer is designing a level exit from a highway. If the coefficient of friction between rubber and wet
concrete is µ = 0.350
3
a. What is the maximum force of friction that the road will apply to a 1200 kg car? (4.12 x 10 N)
2
b. Determine the minimum radius that will allow a car to safely exit at 130 km/h. (3.80 x 10 m)
6. A stunt pilot flies his aircraft in a tight circular path of radius 250 m. If he is flying with a maximum speed of
450 km/h:
a. determine the maximum centripetal acceleration acting on his body. (62.5 m/s2)
b. How many times is the centripetal acceleration greater that normal gravity? (6.37 times)
Vertical Circular Motion
1. A 1.7 kg object is swung in a vertical loop, from the end of a 0.60 m string. If the time taken for one
revolution is 1.1 s what is the tension in the string
a. At the top of the loop (17 N)
b. At the bottom of the loop (50 N)
2. An 826 kg car traveling at a a speed of 14.0 m/s goes over a hill as shown in the diagram. If the radius of the
hill is
61.0 m, what is the force exerted on the road by the car at the crest of the hill? (5.45 x 103 N)
Fn
Fg
3.
You are riding your bike on a track that forms a vertical circular loop. If the diameter of the loop is 10.0 m,
how fast would you have to be traveling when you reached the top of the loop so that you would not fall? (7.00
m/s)
A frictionless rollercoaster does a vertical loop with a radius of
6.0m. What is the minimum speed that the roller coaster must have at the top of the loop so that it stays in
touch with the rail? (7.67 m/s)
5. A popular daredevil trick is to complete a vertical loop on a motorcycle. This trick is dangerous, however,
because if the motorcycle does not travel with enough speed, the rider falls off the track before reaching the
top of the loop. What is the apparent weight of a 66 kg rider traveling at 9.0 m/s at the top of a vertical loop
with a diameter of 10 meters? (422N)
4.
Physics 20
Assignment and Labs
Page
12 6.
If you are swinging a sling with a rock over your head and you want to hit a watermelon in front of you, where
should you release the rock?
Circular Motion Review
5
1. Two asteroids are 5.00 x 106 m apart. If the first has a mass of 6.00 x 10 kg and the second has a mass of
8.00 x 106 kg, compute
a. gravitational force between the two
(1.28 x 10-11 N)
7
-12
b. the change in gravitational force if their separation is increased to 1.50 x 10 m (1.42 x 10 N)
24
6
3
2. What is the weight of a 600 kg object on a 6.00 x 10 kg planet having a radius of 7.00 x 10 m? (4.90 x 10
N)
24
3. A 200 kg satellite is located 9.00 x 109 m from a 6.00 x 10 kg planet. What is the gravitational field due to
the planet at that location? (4.94 x 10-6 N/kg)
4. A 16.0 kg object is moving in a circular path having a 20.0 m radius. If the centripetal force on the object is
200 N, compute the period.
(7.94 s)
3
5. What is the gravitational force on a 20.0 kg mass located 30.0 m due north of a 6.00 x 10 kg object? (8.89 x
-9
10 N)
3
6. A 2.00 x 10 kg car enters a traffic circle, 75.0 m in diameter, at 30.0 m/s. Compute the force on each tire.
(1.20 x 104 N)
7. A 100 kg sphere is moving in a horizontal circle at the end of a 15.0 m long rope. If the sphere completes one
revolution of the circle every 0.0500 s, compute its centripetal acceleration. (2.37 x 105 m/s2)
4
8. A satellite is in orbit about an asteroid. If the orbital radius is 3.00 x 10 m and the period is 10 days, find the
13
mass of the asteroid.
(2.14 x 10 kg)
2
9. A spaceman finds himself in orbit about his spaceship at a distance of 7.00 x 10 m. If the ship has a mass of
6.00 x 103 kg, what is the spaceman's period of revolution? (1.84 x 108 s).
10. An asteroid revolves around the sun with an average orbital radius of three times that of the Earth's. What is
the period of the asteroid in terms of Earth years? (5.2 yrs)
11. It is found that a newly-discovered planet revolves around the sun every 876 days. How far is the centre of the
planet from the centre of the sun in terms of orbital Earth radii? (1.79 Earth radii)
6
12. What is the gravitational field strength on the surface of Venus given that its radius is 6.073 x 10 m and its
mass is 4.88 x 1024 kg? (8.825 m/s2)
13. Calculate the acceleration due to gravity on a 2.00 kg bone if the bone is at an altitude of 150 km above the
planet Pluto. Mass of Pluto 1.20 x 1022 kg. Radius of Pluto 1.15 x 106 m.
(4.74 x 10-1 m/s2)
14. What must be the acceleration due to gravity at a certain altitude above the Earth given that a 3.00 kg can of
soup has a weight of 17.87 N? (5.96 m/s2)
15. What would be the weight of a space monkey having a mass of 32.00 kg given that it is placed at an altitude of
4000 km above the Earth's surface? (119 N)
16. A 900-kg car makes a 180-degree turn with a speed of 10.0 m/s. The radius of the circle through which the car
is turning is 25.0 m. Determine the force of friction and the coefficient of friction acting upon the car. (3.60 x
103N, 0.400)
17. The coefficient of friction acting upon a 900-kg car is 0.850. The car is making a 180-degree turn around a
curve with a radius of 35.0 m. Determine the maximum speed with which the car can make the turn. (17.1 m/s)
Physics 20
Assignment and Labs
Page
13 18. A 1.5-kg bucket of water is tied by a rope and whirled in a circle with a radius of 1.0 m. At the top of the
circular loop, the speed of the bucket is 4.0 m/s. Determine the acceleration, the net force and the individual
force values when the bucket is at the top of the circular loop. (16 m/s2, -24 N, FT=9N, Fg=15N)
19. A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. the ball
makes exactly 2.00 revolutions in a second. What is its centripetal acceleration? (94.7 m/s2)
20. How large must the coefficient be between the tires and the road if a car is to round a level curve of radius 95
m at a speed of 90 km/h? (0.67)
21. A 1.5-kg bucket of water is tied by a rope and whirled in a circle with a radius of 1.0 m. At the bottom of the
circular loop, the speed of the bucket is 6.0 m/s. Determine the acceleration, the net force and the individual
force values when the bucket is at the bottom of the circular loop. (36 m/s2, 54N, Ft=69 N, Fg=15N)
Work and Energy
Pendulum and Roller coasters
1. A 20 cm pendulum is raised to a height of 10 cm above the equilibrium and released. Calculate its speed at the
equilibrium. (1.4 m/s)
2. A 30.0 cm pendulum has a 500 g bob attached to it. It is raised to a 90.0˚ angle with the equilibrium.
Calculate: a) its speed at the equilibrium. b) speed when at 30.0˚ to the vertical (2.43 m/s, 2.26 m/s)
3. A 50.0 cm long pendulum is pushed such that its speed at the bottom is 1.00 m/s. What angle will the
pendulum make with the vertical at its maximum height? (26.1˚)
4. A fully loaded rollercoaster with mass of 3500 kg sits at its highest point (25.0 m above the ground) on the
track. Calculate the maximum speed the rollercoaster could possibly achieve. (22.1 m/s)
5. A rollercoaster is moving at 23 m/s when it is 5.00 m above the ground. Calculate the maximum height of the
rollercoaster. (32.0 m)
6. A rollercoaster has a speed of 8.00 m/s when it is 2.00 m above the ground. It started from the highest point of
15.0 m above the ground. What is the force due to friction if the distance between these two points is 500
mand the cars have a total mass of 3000 kg? (573 N)
Projectile Motion
1.
A 2.00 kg projectile is fired from a small cliff 50.0 m above level ground. The projectile is fired at 100 m/s at
30.0˚ above the horizontal. Calculate
3
a. vertical Ek when the projectile is 20.0 m above level ground (3.09 x 10 J)
b. The vertical speed when the projectile is 20.0 m above level ground (55.6 m/s)
Physics 20
Assignment and Labs
Page
14 2.
Given the system below, calculate the speed of the ball at point A. (14.0 m/s)
a. What speed would it require at point A to reach point B? (22.1 m/s)
3.
A 2.00 kg ball was fired straight upward with an initial speed of 200 m/s.
3
a. Compute the maximum height reached (2.04 x 10 m)
b. Compute the ball’s speed at a height of 400 m (179 m/s)
A cannonball was fired horizontally from the top of a cliff. If the initial speed of the ball was 50.0 m/s and the
cliff is 150 m high, compute the vertical speed of the ball just before impact (54.2 m/s)
How many joules of heat are produced by a 2.00 kg body when it falls through a distance of 3.00 m and comes
to rest on the floor? (58.9 J)
A 2.00 kg object is thrown upward from a point 10.0 m above the earth’s surface at an angle of 45.0˚ with the
horizontal with a horizontal speed of 10.0 m/s.
a. What is the upwards Ek (100 J)
b. What is its vertical velocity when it is 5.00 m above the earth’s surface? (14.1 m/s)
A small 2.00 kg ball is placed in a large bowl as shown in the diagram. Point A has a height of 6.00 m and
point B has a height of 8.00 m.
a. Compute the maximum speed that the ball will attain if released from position A. (10.8 m/s)
b. What speed must the ball have at point A if it is to leave the bowl? (6.26 m/s)
4.
5.
6.
7.
B
A
8.
A 6.00 kg rock was dropped off a 70.0 m high cliff. How many joules of heat would be released supposing
that all of its energy were converted to heat? (4.12 x 103 J)
Power
1. A piano has a mass of 400 kg. It is dragged at a constant velocity, 8.00 m across a level floor where the
coefficient of friction is 0.650. It takes 3.00 minutes to move the piano. Calculate the power output. (113 W)
2. A 55.0 kg sofabed is lifted to the fourth floor apartment balcony (14.0 m) in 7.00 minutes. Calculate the
power output. (18.0W)
3. A 100 kg refrigerator is placed upon a moving dolly and rolled at a constant velocity up an incline ramp into a
moving truck. The ramp is 5.0 m long and the truck bed is 1.2 m above the ground. The force of friction from
all sources is 65.6 N. Calculate the power output of the workers if it takes them 45 seconds to accomplish
the move. (33 W)
4. A motorcycle’s engine exerts and average force of 1790 N while putting out 40.0 hp ( 1 hp = 746 Watts).
Calculate the average constant velocity, in km/h, the motorcycle is able to maintain. (60.0 km/h)
5. An electric hot water heater contains 150 L of water. (density of water is 1.00 kg /L) The formula for
calculating the energy required to change the temperature of water is, E = mc∆T where m is mass of water in
grams, c is a constant (4.19 J/g ºC) and ∆T is the change in temperature. It takes 30 minutes to heat a full
tank of water from 20ºC to 80ºC. Calculate:
a. the power rating of the heating elements in the hot water tank. (2.10 x 104 W)
b. the cost of heating the water if electricity cost 15.0 ¢ / kWh. (157¢)
Physics 20
Assignment and Labs
Page
15 Extra Practice for Work and Energy
1. A 2.00 kg object is dropped from a cliff 4.00 x 102 m high. Determine the:
a. vertical speed of the object just prior to impact (88.6 m/s)
b. vertical speed when it falls 150 m (54.2 m/s)
2. The coefficient of sliding friction between a 900 kg car and pavement is 0.80. If the car is moving at 25 m/s
along level pavement when it begins to skid to a stop, how far will it go before stopping? (40 m)
3. Just before striking the ground, a 2.00 kg mass has 400 J of Ek. If friction can be ignored, from what height
was it dropped? (20.4 m)
4. A 0.500 kg ball falls past a window that is 1.50 m in vertical length.
a. How much did the Ek of the ball increase as it fell past the window? (7.35 J)
b. If its speed was 3.0 m/s at the top of the window, what was it at the bottom? (6.2 m/s)
5. Consider the simple pendulum having a 75.0 cm length. If it is released from a point which makes a 90.0˚ with
the vertical,
a. what will be the speed of the ball as it passes the lowest point? (3.84 m/s)
b. What is the ball’s speed when the pendulum makes an angle of 37.0˚ with the vertical? (3.43 m/s)
6. A 1200 kg car coasts from rest down a driveway that is inclined 20.0˚ to the horizontal and is 15.0 m long.
How fast is the car going at the end of the driveway if
a. friction is negligible (10.0 m/s)
b. a friction force of 3000 N opposes the motion? (5.06 m/s)
7. There is a bead sliding on a wire. From what height is the bead dropped if it has a speed of 200 cm/s at the
bottom? Ignore friction. (20.4 cm)
8. A 3.00 g bead is dropped from a height of 50.0 cm along a wire to a point that is 30.0 cm from the bottom and
stops. The length of wire between where the bead starts and ends is 400 cm. How large an average friction
force opposed its motion? (1.47 x 10-3 N)
9. An 80.0 kg object is fired straight upward with a speed of 120 m/s. Compute the maximum height reached.
(734 m)
10. A projectile is fired at 3.00 x 102 m/s at an angle of 60.0˚ above the horizontal. Find the
a. maximum height reached (3.44 x 103 m)
b. time of flight (53.0 s)
c. horizontal distance traveled (maximum) (7.95 x 103 m)
11. A 15.0 kg object moving at 10.0 m/s is subjected to a force of 20.0 N opposing this motion. If the force acts
over a distance of 25.0 m, find the final velocity of the object? (5.77 m/s)
12. A 25 N force moves a 10 kg stationary object through 3.0 m in 1.6 s.
a. How much work is done by the force? (75 J)
b. What is the final velocity of the object? (3.9 m/s)
13. A force of 3.00 N acts through a distance of 12.0 m in the direction of the force. Find the work done. (36.0 J)
14. A 4.00 kg object is lifted 1.50 m.
a. How much work is done against gravity? (58.9 J)
b. Repeat if the object is lowered instead of lifted. (58.9 J)
15. Compute the useful work done by an engine as it lifts 40.0 liters of tar 20.0 m. One liter of tar has a mass of
1.07 kg. (8.40 x 103 J)
16. How large a force is required to accelerate a 1300 kg car from rest to a speed of 20.00 m/s in a distance of
80.00 m? (3250 N)
17. A 1200 kg car going 30 m/s applies its brakes and skids to rest. If the friction force between the sliding tires
and the pavement is 6000 N, how far does the car skid before coming to rest? (90 m)
18. A 200 kg cart is pushed slowly up an incline. How much work does the pushing force do in moving the object
up along the incline to a platform 1.50 m above the starting point if friction is negligible? (2.94 x 103J)
Physics 20
Assignment and Labs
Page
16 Force (N)
19. Repeat the above problem if the distance along the incline to the platform is 7.00 m and a friction force of 150
N opposes the
Force vs Distance
motion. (3.99 kJ)
.
20. A machine is used to
30
accelerate 6.00 kg
stationary cart. If the
25
cart is accelerated
over a distance of
14.0 m and the
20
machine exerts force
as
shown by the graph
15
below, what is the
final speed of the
10
cart?
(10.0 m/s)
5
0
0
2
4
6
8
10
12
14
Distance (m)
21. A 60 kg woman walks up a flight of stairs that connect two floors 3.0 m apart. Standard stairs are inclined at
33˚ .
a. How much work is done by the woman in lifting the object? (1.8 kJ)
b. By how much does the woman’s Ep change? (1.8 kJ)
c. Assume the women walks at a constant speed of 1.25 m/s and that the coefficient of friction is 0.800
for the entire horizontal distance she travels. Calculate the average total force her lags must apply to
climb the stairs. (716N)
d. What power does her legs generate? (162W)
22. A pump lifts water from a lake to a large tank 20 m above the lake.
a. How much work against gravity does the pump do as it transfers 5.0 m3 of water to the tank? Once
cubic meter of water has a mass of 1000 kg. (9.8 x 105 J)
b. If the water is lifted in 15.0 s, what is the power output of the pump?
23. A driver of a 1200 kg car notices that the car slows from 20.0 m/s to 15.0 m/s as it coasts a distance of 130 m
along level ground. How large is the force that opposes the motion? (808 N)
24. A 2000 kg elevator rises from rest in the basement to the fourth floor, a distance of 25.0 m. As it passes the
fourth floor, its speed is 3.00 m/s. There is a constant frictional force of 500 N. Calculate the work done by
the lifting mechanism.
(5.12 x 105 J)
Physics 20
Assignment and Labs
Page
17 Physics 20 Uniform Motion
(25 Marks)
Title Page:
Include the title of the lab, your name underlined, lab partner's name, the class and due date.
Objective:
The objective is to illustrate constant motion by constructing graphs of distance versus time and
velocity versus time for the uniform motion (constant speed) from the data obtained using the air table.
Apparatus:
The air table.
Procedure:
Level off the table as much as possible. Place one puck in the top right hand corner on a folded piece
of paper (only one puck is used for this experiment). Push the other puck and simultaneously activate the sparktimer.
Both pucks must be on the paper to complete the circuit. Set the timer to 50 ms.
Observations:
- Staple data sheet onto back of lab write up.
Analysis:
A. Distance v Time Graph :You will determine when the spacing of the dots seems to be constant. You will identify
the first dot of this section as point zero. From this point measure the distance to all other points using units of
millimeters. You will make a table of values of this information. You will plot this information in the form of a
distance - time graph. Only the graph is to appear on the graph paper. It must be done only in pencil. (10 marks)
Ensure that you include the following:
• Table of values.
• Graph.
• Calculation of slope including showing triangle used on graph. (include units)
• What does the slope of a distance-time graph represent? Answer in a complete sentence.
• From your graph, write the equation for the line.
B. Check results
Calculate the average velocity for the entire run using an equation learned in class. Ensure that you include the
following:
• Show the calculation for the above.
• Compare this value with the slope obtained from the distance v time graph.
C. Uniform Motion Graph
Determine the average velocity during each time interval and make a graph plotting it against the midpoint of the time
interval. Ensure that you include the following:
• Sample calculation of average velocity for time period between 200ms and 250ms
• Table of values.
• Graph.
• Calculate the area under the curve (line) between the times of 200ms and 300ms
• What does the area of a velocity-time graph represent? Answer in a complete sentence.
• From your air table data sheet, calculate the actual distance between 200ms and 300ms?
• From the graph, determine the initial velocity of the puck.
D: Conclusion
Ensure that you include the following:
• Restate objective. "The objective of this lab was to"
• Discuss your results in a paragraph and include answers to these sample questions. Did this lab satisfy the
objective? Why/ why not? Are the graphs representative of an object moving with a uniform speed? Why/
why not?
Note: One mark will be deducted if the contents are not in the above-mentioned order.
: One lab of the group will be marked at random and the entire group will receive that mark.
Physics 20
Assignment and Labs
Page
18 Physics 20 Uniform Acceleration Lab
(24 Marks)
Title Page:
Include the title of the lab, your underlined name, lab partner's name, the class and due date.
Objective:
The objective of the lab is to construct graphs that are representative of an accelerating body.
Apparatus:
The air table.
Procedure:
Tilt the air table by placing a book under one of the legs. Make sure that one of the pucks is placed
on a folded corner of the paper on the air table. Set the timer to 50 ms. Place the other puck on the elevated side of the
table. Release the puck and simultaneously start the timer. Continue pressing the timer-starter until the puck reaches
the other end of the table.
Observations:
- Staple data sheet onto back of lab write up.
Analysis:
A.
You will identify the first dot as the zero point. From this point measure the distance to all other points using
units of millimeters. You will plot this information in the form of a distance - time graph.
(1)- Table of values.
(4)- graph.
B. Determine the average velocity during each time interval and make a graph plotting it against the midpoint of the
time interval.
(1)- Sample calculation of average velocity for time period 200ms - 250ms
(1)- Table of values.
(4)- graph.
(1)- From the graph, determine the initial velocity.
(1)- What does the area of a velocity-time graph represent? Answer in a complete sentence.
(2)- Calculate the area under the line between time t= 200ms and 350ms
(1)- Calculate the actual distance covered, using the initial data, btween the time period t= 200ms and 350ms.
C. Determine the acceleration of the puck.
(3)- Using the velocity-time graph only.
(1)- Write the equation of the line for the velocity-time graph.
Conclusion: In a paragraph or two, discuss your results and include the answers to the following questions.
Restate objective.
(1)- What did you notice about the spacing between dots as the time increased?
(1)- What was the shape of the distance-time graph?
(2)- Are these graphs representative of an accelerating object? Comment on each graph.
Note: One mark will be deducted if the contents are not in the above-mentioned order.
:The graphs should be large and done only in pencil.
:Nothing other than the graphs should be on the graph paper.
:One lab per group will be marked but each member must hand in a complete lab.
Physics 20
Assignment and Labs
Page
19 Frictional Force Lab
Objective To measure the coefficient of friction for a particular system Theory A mass pulled along at a constant speed is not accelerating. This means that the force that is being applied only needs to overcome friction. Materials a block of wood with hook and string attached force meter LabQuest handheld Procedure 1. Plug force meter into the LabQuest device and plug device into a wall socket. 2. Turn on the LabQuest handheld device. a. Zero the force meter by tapping the readings area and then zero 3. Hang the block of wood from the device and record the weight of the wooden block. On / Off button
Start recording
button
Set the wooden block, force meter and LabQuest on a level surface. Push the start recording button. Pull the wooden block at a constant speed for 3-­‐5 seconds. A graph will appear when 10 seconds have elapsed. Tap ‘analyze’ on the screen à statistics à force. Then highlight an area of the graph that appears to be flat. 9. Record the mean force for this area. 10. Add mass to the block and repeat. Continue for 10 measurements. Masses of 100 g and more work best. Analysis Graph your results with force applied as a function of the weight pulled. Calculate the slope of the line of best fit. Conclusion In a paragraph, discuss your results. Did you achieve the lab objective? Discuss how you know this. What are possible sources of error? 4.
5.
6.
7.
8.
Physics 20
Assignment and Labs
Page
20 Power Output of Vehicles
Each person must hand in a complete project and no two can use the same vehicle data.
Objective: Compare the stated power of a vehicle’s engine to the performance of the vehicle using Excel graphs.
Data collection
You will obtain vehicle performance data and calculate the following.
Velocities for at least 6 accelerations.
Using the curb weight of the vehicle and the velocities from above, calculate the kinetic energy for these same 6 times.
Analysis
Using Excel, graph the data, kinetic energy as a function of time. Calculate the slope of the line. Write the equation of
the line.
You must include a sample calculation for the velocity conversions and the kinetic energy calculation.
You may require the following data to convert these measurements.
1 kg = 2.205 lbs
1 mph = 0.447 m/s
1 hp = 745.7 W
Compare the stated power (bhp) to the calculated power from your graph. State this as a percentage.
"
%
calculatedpower
Conclusion
$
' x100
Discuss your
results. You should include a statement about why your graph does
# statedpower &
not pass through
the origin as well as why you think the motor does not produce
100% of the stated horse power.
Using Excel
!
1. Open an Excel workbook.
2. Title the variables you are going to plot. Place the x-variable first.
3. Click Insert à chartà scatter plotà choose the first option.
4. Ensure that your formatting palette is open. In chart options of this palette label the title, y-axis and x-axis.
5. Click on a data point. (They should all become highlighted.) Then go to chartàadd trend line.
6. The Trendline formatting box should open automatically. If it did not, then double click on the line. Choose
optionsà display equation. The equation will be shown in general form. Double click on the formula and
replace the y and x with the appropriate variable.
7. You can make the line go to the x or y- axis by selecting forecast backwards. Do this until the line reaches the
axis.
Email project (excel file) to [email protected]
Physics 20
Assignment and Labs
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21 Circular Motion and Gravitation Lab
Name: _____________________________
.
rubber
stopper
Partners: ___________________________
Total marks _______ of 15
Objective:
Use circular motion in determining the mass of the
stopper by equating Fnetc to Fg.
paper clip
Procedure:
1. Measure the mass of the washers.
2. Measure the distance from the middle of the
washers
stopper to the top of the plastic handle and
record this measurement as the radius of circle
below.
3. Practice whirling the stopper in a circular horizontal path above your head. The stopper is traveling at the
desired speed when the weight of the washers supplies the force needed for the stopper to maintain its circular
path at the desired radius.
4. When the stopper is moving with the desired rotational speed, have your lab partner use the stopwatch to
measure the time it takes the stopper to complete 30 revolutions. Record this time on the data sheet. Repeat
this step two more times.
5. Calculate the average time for one revolution of the stopper. This is the period of revolution.
6. Add 2 or three washers and Repeat for 5 more trials.
Student Responsibility
Each student must hand in one lab write up.
Observations: Radius of circle: ______
Trial 1: mass of washers______
Time for 30 revolutions (trial 1): __________ (trial 2): __________ (trial 3): __________
Trial 2: mass of washers______
Time for 30 revolutions (trial 1): __________ (trial 2): __________ (trial 3): __________
Trial 3: mass of washers______
Time for 30 revolutions (trial 1): __________ (trial 2): __________ (trial 3): __________
Trial 4: mass of washers______
Time for 30 revolutions (trial 1): __________ (trial 2): __________ (trial 3): __________
Trial 5: mass of washers______
Time for 30 revolutions (trial 1): __________ (trial 2): __________ (trial 3): __________
Trial 6: mass of washers______
Time for 30 revolutions (trial 1): __________ (trial 2): __________ (trial 3): __________
Analysis
Show all of your work for one trial.
Period: __________ Velocity:_________
Physics 20
Assignment and Labs
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22 Complete the table.
Trial
Fg
T
v
v2
Graph v2 as a function of gravitational force.
Calculate the slope of the line on your graph.
Physics 20
Assignment and Labs
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23 Using your slope to calculate the mass of the stopper.
Actual mass of the stopper ___________.
Conclusion:
Calculate the percentage error in the mass of the stopper between the experimental and actual value. Show all work.
% error (difference) = | actual - experimental |
actual
x 100
Identify possible sources of experimental error (these are not measurement errors!) and discuss, in a sentence or two,
how this would affect your results.
Physics 20
Assignment and Labs
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24 Calculating Work for a Spring
Problem:
How is work on a spring determined from a force-distance graph?
Purpose:
To determine the amount of work done in stretching a spring.
Materials:
springs
force meter
ruler
board with nail
Procedure:
1. Place the spring on the nail and attach the force meter to the other end. Take the slack out of the spring.
2. Label the point where the spring and the meter are as the starting point.(distance= 0)
3. Construct a table of values that clearly identifies the force required to stretch the elastic in consecutive, equal
interval distances. (for example: stretch the elastic 0.5 cm and record the force required to do this.) You must
have 6-10 data points.
4. Graph the data and draw the line of best fit. You may ignore the first two points if they keep the line of best fit
from being a straight line.
Analysis:
1. Table of values for the force and distance the elastic stretched.
2. Graph the data with the manipulated variable on the x axis.
3. Calculate the area under the line of best fit.
4. Compare the above value to W= Fmaxd / 2. Should it be the same? Explain.
5. Calculate the % difference.
[experimental - theoretical (formula) / theoretical] x 100
6. From the graph only, determine the work required to stretch the elastic from 2.0 cm to 5.0 cm.
7. Calculate the slope of your line. What does the slope represent?
8. Write the equation of the line for your graph.
Conclusion:
Restate the objective. In a few sentences discuss the problem and purpose in relation to this experiment. In
your discussion address the following:
i)
Was the force required to stretch the elastic constant? Use information from your graph to support
your answer.
ii)
Include any experimental sources of uncertainty.
You must have a title page for the group with your name and each lab partner's name on it. One mark will be deducted
if title page is not included.
Note: Each student is to hand in one lab report. Only one of the group will be marked and all members will receive
the same mark. Ensure that all members have the complete information.
Physics 20
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25 Period of a Pendulum
Perform the experiment as outlined in the following cartoon.
This is a self-discovery lab in which you will explore the relationship between the length of a pendulum, the mass of
the bob, and the period of oscillation. Base your procedure upon the cartoon.
Keep the swing arc small (less than 20˚).
You will write, design, and perform an experiment that satisfactorily investigates the relationships outlined above.
Your lab must include a title page, a problem, a hypothesis (including any predictions), experimental design (a brief
description of the steps taken, the variables (controlled responding, and manipulated) and a list of materials used),
detailed procedure, observation and measurement
(recorded in a table) and analysis of the data including
a graph and a conclusion (discussion of the results, percent error, and any possible source of error).
Good experimental analysis includes a prediction. At the end of the write up, predict the length and mass required to
have a pendulum that will swing with a period of 1.00 s.
Marks will be distributed as follows:
(4) Design an experimental procedure, including an equipment list, that will compare the length of pendulum, the
mass of the bob and the period of oscillation.
(2) Record the results of your experiment in a table.
(5) Analysis and interpretation of your results, including the graph.
(4) Conclude by restating your objective and summarize your results.
(2) Prediction of the length and mass required for a period of 1.00s.
17 marks in total
Physics 20
Assignment and Labs
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26 Vertical Spring Lab Question: How do Hooke’s Law and the conservation of energy apply to a mass oscillating on a vertical spring? Objective: collect data to determine the spring’s constant, the period of oscillation, and the speed of the mass to verify that energy is conserved in this isolated system and that Hooke’s law is obeyed. Materials: Spring Vernier motion detector Masses Computer with Logger Pro
Stop watch Experimental design: place various masses on a spring and measure the distance the spring stretches. Graph the data to determine the spring’s constant. Oscillate the spring and record the data using the motion detector and software. Measure the period. Measure the amplitude and compare it to the calculated value. Part 1: determine spring’s constant Procedure: 1. Obtain the spring apparatus and set it up as demonstrated by your teacher. 2. Move the ruler so that the needle points to zero. This is your initial position. 3. Add one 10 gram mass and record the new position. 4. Repeat this with four more masses (if your spring can safely handle more, you may continue to add mass). Observations: Record the data in a table Analysis 1. Graph the stretch of the spring as a function of the force. 2. Calculate the slope of the graph. Conclusion 1. What forces are working on the spring as you add mass? Write the equation. 2. What are the units of your slope and how does this work into your equation from above? 3. Calculate the spring’s constant from your graph. 4. On this graph, what does the y-­‐intercept represent? Part 2: determine the period Procedure: 1. Place three or four 10 gram masses on the spring. 2. Pull the mass assembly down 2-­‐3 cm and release. 3. Time ten oscillations. 4. Repeat this at least two more times. Observations Record the time for each trial. Calculate the average time for ten oscillations. Analysis 1. Calculate the time for one oscillation. 2. Compare your measured period to the theoretical value, using the spring constant calculated in part 1. (only if you have already discussed the period of a spring in class.) Hand in one lab per group. Physics 20
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27 Each Member of the Group must keep a copy of the print out from this portion! Do not hand this part in at this time! Part 3: determine the wave nature and energy of the oscillating spring Procedure: 1. Set up the spring such that it is suspended between 0.5 and 1.0 m above the motion detector. WARNING: ensure that nothing is obstructing or interfering with the motion detector. It is best to hang the mass and spring over the edge of the desk or chair. spring
motion
sensor
2. Open the LoggerPro application on the computer you have been assigned to use. 3. Open the file menu and the physics with Vernier and 02 spring.cmbl 4.
5.
6.
7.
Plug USB into computer and other end to GoMotion detector. Let the assembly hang freely and run the motion detector to obtain an equilibrium measurement. Add three or four masses(same number as in part 2) and start the spring oscillating. Collect data by pushing the green triangle in the corner. You should get a smooth wave pattern. If not, check to ensure that there is nothing that is interfering with the motion sensor. The sensor sends out ultrasonic waves that spread out about 30˚. Observation Use autoscale (under analysis). Print your graph and data. Analysis 1. On the graph: a. Label the equilibrium, amplitude, and one cycle. b. Compare where the maximum speed occurs with its position. Show this on your graphs. c. On the position graph, label where the speed is zero. 2. On the data table: a. Find and label where the speed in greatest and least. b. Calculate the period and the amplitude from the data in the table. Physics 20
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