Download Unit 2 Assignments

Unit 2 Lesson 1
Exercises
1. A rope is attached to a 2.0 kg rock and pulled. Write a net force equation if
the mass is a) accelerating up
( T - mg = ma)
b) accelerating down
(mg - T = ma)
c) Find the cord tension if the mass is accelerating at
i) 0.0 m/s2
(20. N)
ii) 1.0 m/s2 UP
( 22 N)
2
iii) 2.0 m/s DOWN
(16 N)
iv) 9.8 m/s2 DOWN
(0.0 N)
T
2 kg
Fg
2. Find the acceleration of the mass if the cord tension is
a) 30. N
b) 19.6 N
c) 9.6 N
string
2 kg
(5.2 m/s2 up; 0.0m/s2; 5.0 m/s2 down)
3. In the diagrams below, assume the force F is the only horizontal force on the
block. If the first block accelerates at rate a, then find an expression for the
unknown acceleration.
(a/2,2a)
acceleration = ?
acceleration = a
F
F
2M
M
frictionless surface
acceleration = a
acceleration = ?
2F
F
M
M
frictionless surface
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©Donald J. Mathewson 2002
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4. A parachutist free-falls for a while and then opens their parachute. If the
force of air resistance from the parachute is equal to the weight of the person,
then which of the following is true?
a) the person slows down
b) the person speeds up
c) the person moves at a steady speed
explain your answer using principles of physics
5. A cyclist is moving to the right steadily at 8.2 m/s. If the force of air drag is
130 N, then what is the force of propulsion from the road?
(130 N right)
6. A mass is being pulled up by a cable. If the mass is moving up and slowing
down, compare the forces that act on the mass and write a net force equation
(mg>T ; mg- T = ma)
T
Fg
7. Find the weight of a 80.0 kg person
a) on the Earth
b) on the Moon
c) 2000. km above the surface of the Earth, where g= 5.70 N/kg
(784 N; 128 N; 456 N)
8. An object in free-fall experiences only the force of gravity. for such an
object
a) draw a force diagram
b) write a net force equation
(mg = ma)
c) solve for the acceleration
(a= g)
9. A 75 kg mountain climber free-falls for 10.0 metres, then reaches the end of
his safety rope. The rope stretches and stops the climber with 1.25 seconds.
a) find the speed of the climber when the rope begins to stretch (14.0 m/s)
b) write a net force equation for the 'slow down' by the rope (T-mg = ma)
c) find the force from the rope (1580 N)
10. Add the force vectors to find the net force and direction:
6250 N North and
3500. N, 30.0° S of West
(5420 N; 56.0° N of W)
Physics 12 Student Workbook
©Donald J. Mathewson 2002
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Unit 2 Lesson 2
Exercises
1. A 25.0 kg child is standing on a bathroom scale which reads in kg. The scale
reads 32.0 kg. Describe the motion of the child. (2.74 m/s2 acceleration up)
2. A person stands in an elevator. Write a net force equation in each case
a) elevator at rest
b) elevator accelerates up
c) elevator moves up at constant speed
d) elevator moves down at constant speed
e) elevator accelerates down
(F N=mg; FN-mg=ma; F N=mg; FN=mg; mg-FN=ma)
3. A 55.0 kg student is in an elevator accelerating up at 2.50 m/s2 .
a) write a net force equation
(F N-mg=ma)
b) what would a force scale placed under their feet read?
(676 N)
4. A 25 kg mass is falling and accelerating downwards
a) write a force equation
(mg-F air = ma; 65 N)
b) What is the force of air resistance if the acc'n is 7.2 m/s2 DOWN
5. a) A 5.00 kg rock is moving upwards on the earth and it experiences 5.00 N of
air drag. Find its acceleration.
b) A 5.00 kg rock is moving downwards on the earth and it experiences
5.00 N of air drag. Find its acceleration.
c) The same rock is thrown downwards on the moon. Find its acceleration.
(10.8 m/s2 down; 8.8 m/s2 down; 1.6 m/s2 down.... no air on moon!)
6. Find the acceleration if the applied force is
a) 5 N
(0.5 m/s2 LEFT)
b) 10 N
(0 m/s2)
c) 20 N
(1 m/s2 right)
applied
Force
10 N
friction
10 kg rock
7. A 200. kg spaceship speeds up from rest to 250. m/s in 0.200 seconds. Assume
there is no air friction and find
a) the acceleration using kinematics
(1250 m/s2 )
b) the force from the engines
(2.50 × 105 N )
8. A 250. gram ball is moving to the left at 25.0 m/s. A person catches it and
stops it in 0.320 seconds. Find the horizontal force and direction exerted on the
ball by the person's hand.
(19.5 N right)
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©Donald J. Mathewson 2002
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9. A 55.0 kg parachutist is falling at constant speed. What force of air
resistance acts on the person?
(539 N up)
10. A 10. kg mass (initially at rest) is pulled with a force of 30. N across a 8.0 m
long rough surface. The force of friction from the surface is 10. N.
a) given that the mass accelerates right, write a net force equation
b) Find the acceleration of the mass.
c) find the final speed of the mass
(T-Ff=ma; 2.0m/s2;5.6 m/s)
rope
10 kg
rough surface
11. A plane flies north at 700. kph. The wind blows towards the East such that
the resultant motion of the plane is along the line 20° E of N. Find the resultant
speed of the plane.
(745 kph)
12. A 12 000. kg rocket accelerates straight upwards from the surface of the
Earth. Find the thrust force from its engines if it is accelerating at 24.0 m/s2.
(4.06 × 105 N)
13. A mass is thrown at an angle on flat ground. Sketch a graph showing the
a) vertical velocity as a function of time
b) horizontal velocity as a function of time
14. A parachutist jumps out of a plane and free falls. They reach terminal
speed and maintain that speed for a while. Then they open their parachute.
They quickly reach a different terminal speed and descend to the ground.
Sketch a force- time graph. Explain for each section of the graph in a few
words what is happening to the object.
Physics 12 Student Workbook
©Donald J. Mathewson 2002
88
Unit 2 Lesson 3
Exercises
1. A force of 400. N is required to start a box moving across the floor (so
friction must be about 400 N). If the box has mass 40.0 kg, find the friction
coefficient
(1.02)
2. A 20.kg box sits on a floor with µ=0.30 . What force is required to move the
box across the floor
a) at steady speed
(58.8 N )
2
b) accelerating at 1 m/s (78.8 N)
3. A mass of 125 kg is being pulled to the right across a rough floor with an
applied force of 200. N. Find the coefficient of friction if the acceleration of
the mass is a) 0.0 m/s2
(0.163)
2
b) 1.50 m/s right/speeding up
(0.0102)
c) 2.20 m/s2 left/slowing down
(0.388)
4. Find the acceleration of a 100. kg dragster if its tires have µ=0.80. (7.8 m/s2)
5. A 50.0 kg rollerblader moving at 3.00m/s drags a foot on the ground to stop.
If µ= 0.300, how far does the rollerblader go before stopping? (1.53 m)
6. A car is moving at speed v on a road with friction coefficient µ. Show that
v2
the stopping distance is given by d =
2µg
7. A 10. kg box sits on a floor with µs =0.25 and µk =0.20. Find the acceleration if
the box is pulled with a) 15 N b) 22 N c) 30. N ( 0m/s2; 0 m/s2; 1.0 m/s2)
8. . A 50.0 kg block is pushed with a force of 60.0 N across a 20.0 metre long
floor. The first 10.0 metres of the floor are frictionless, but the last 10.0 metres
have µ=0.350. Describe the motion of the block
(4.90 m/s after 10m, then goes 5.38 m further and stops)
9. A 50.0 kg person falling at 8.00 m/s hits the floor and stops in 0.0500 seconds.
Find the force that the floor exerts on this person.
(8490 N)
10. A 55.0 kg person stands on a newton scale. Find the scale reading in each
case
a) elevator at rest
b) elevator accelerates up at 1.00m/s2
c) elevator moves up at constant speed
d) elevator accelerates down at 1.00 m/s2
e) elevator accelerates down at 9.80 m/s2 (free fall)
(539N; 594 N; 539 N; 484 N; 0N )
11. Find the speed when this projectile hits the ground
(17.9 m/s)
5.00 m/s
15.0 m
Physics 12 Student Workbook
©Donald J. Mathewson 2002
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Unit 2 Lesson 4
Exercises:
(2m/s2, 8 N)
1. Find acceleration and cord tension
12 N
2 kg
4 kg
µ=0
(4.0 m/s2; 48 N)
2. Find acceleration and cord tension
60. N
3 kg
12 kg
µ=0
(1.5 m/s2)
3. Find acceleration
21. N
6.0 kg
8.0 kg
µ=0
(3.0 m/s2; 12 N; 18 N)
4. Find acceleration and cord tensions
4.0 kg
2.0 kg
36 N
6.0 kg
µ=0
5. Find acceleration and cord tension
(3.3 m/s2; 13 N)
4.0 kg
µ=0
2.0 kg
6. Find acceleration and cord tension
(8.2 m/s2; 33 N)
4.0 kg
µ=0
20. kg
Physics 12 Student Workbook
©Donald J. Mathewson 2002
101
7. Write force equations for each mass
3.00 kg
6.00 kg
(T1-11.76 = 6a; 30 - T1-5.88 = 3a)
30.0 N
µ = 0.200
8. Write force equations for each mass
(T1 - 5.88 = 6a; 29.4 - T1 = 3a)
6.00 kg
µ=0.100
3.00 kg
9. a) write force equations for each mass
b) find acceleration and cord tension
(T1 - 11.76 = 12a; 39.2 - T1 = 4a)
(1.72 m/s2; 32.3 N)
12.0 kg
µ=0.100
4.00 kg
10. a) write force equation for each mass
b) find acceleration and cord tension
(30-T -3.92=4a; T-19.6 = 20a)
(0.27 m/s2; 25 N)
30. N
4.0 kg
20. kg
µ = 0.10
(4.1m/s2)
11. Find the acceleration of the system
2.0 kg
3.0 kg
µ=0.16
Physics 12 Student Workbook
©Donald J. Mathewson 2002
5.0 kg
102
12. The blocks below are made of different materials and have different
coefficients of friction.
a) write force equation for each mass (T1-2.94 = 3a; T2-T1-31.36=4a;117.6-T2=12a)
b) solve for acc'n and tensions
(4.4 m/s2; 16 N; 65 N)
3.0 kg
4.0 kg
µ=0.80
µ=0.10
12 kg
13. In the system below, the 2.0 kg moves with the 12 kg, ie. they accelerate as
a system. Find the acceleration of the system and then find the coefficient of
friction of the 2.0 kg. (3.6 m/s2; 0.36)
2.0 kg
12 kg
µ= 0
8.0 kg
14. If the mass system below is accelerating upwards at 1.75 m/s2, find the
tension in the two cords.
(upper:80.8 N; lower: 57.8 N)
2.00 kg
5.00 kg
15. A person (M) sits in a platform chair (m) and pulls themselves up using the
rope. Write force equations for the person, chair and system
fixed pulley
person M
platform chair m
{T+FN-Mg=Ma; T-FN-mg=ma: 2T-(M+m)g=(M+m)a }
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Unit 2 Lesson 5
Exercises
1. The same water bottle from example #6 is now filled and thrown upwards.
What will happen as the bottle is rising?
leaky water bottle
after being thrown
upwards.
what happens as it
rises?
leaky water bottle
A) the water stops leaking out
B) the water leaks out at the same rate
C) the water leaks out faster
Using principles of physics explain your answer.
explanation: _________________________________________________________
_________________________________________________________
_________________________________________________________
2. Find the acceleration of these systems (2.3 m/s2; 4.9 m/s2)
3.5 kg
3M
5.7 kg
M
3. Find the acceleration and the tensions (1.96 m/s2; 39.2 N; 3.92 N)
5 kg
3 kg
2 kg
Physics 12 Student Workbook
©Donald J. Mathewson 2002
frictionless surface
109
4. A 55 kg person pushes on the floor with 800. N of force for 0.25 seconds. How
high do they jump off the ground? (7.2 cm)
5. A 40.0 kg table is on a floor with µk =0.270 and µs=0.310. Find
a) the force required to move the desk (121 N)
b) the acc'n of the desk if it is pushed with 150. N (1.10 m/s2)
6. A diver jumps from a height of 24.0 metres into a swimming pool
a) find her speed when she enters the water
(21.7 m/s)
b) if the diver stops after sinking 3.00 metres into the water, find the acc'n in
the water
(78.4 m/s2)
7. Two rocks are dropped off a cliff, the second 1.600 seconds after the first.
How far below the cliff is the second stone when the rocks are 36.00 m apart?
(10.97 m)
8. The system shown below is at rest. Find the normal force exerted by the
table (18N)
5.0 kg
table
3.2 kg
9. There is humourous tale told of a worker who is caught in a pulley system,
and pulled to the top of the system. The impact of the load stops the system
within 0.15 seconds, but it causes half of the load to break off. The worker is
then heavier and falls. The worker hits the ground, and stops within 0.50
seconds. Then he lets go of the rope and remaining load falls onto his head.
Find the total time for this accident to occur. (7.42 sec)
80.0 kg
load
6.50 m
60.0 kg
worker
60.0 kg
worker
40.0 kg
load
40 kg
breaks off
Physics 12 Student Workbook
©Donald J. Mathewson 2002
lets go
of rope
60.0 kg
worker
110
Unit 2 Lesson 6
Exercises
1. Consider a 10. kg mass on a 20.° incline plane that is not moving.
a) draw force diagram and write force equations
b) find normal force, friction force and µ
(F N=mgcos(θ); mgsin(θ)-F f =ma; 92 N; 33 N; 0.36)
10. kg
20°.
2. A 5.00 kg mass slides down a 20.0° incline with µk =0.150.
a) write force equations (F N=mgcos(θ); mgsin(θ)-F f =ma)
b) Find the acc'n
(1.97 m/s2)
3. A 8.0 kg mass is on a 12 metre long 35° slope with µk =0.20. Find
a) acc'n
b) time to slide down slope
c) speed at bottom of slope
(4.0 m/s2; 2.4 s; 9.8 m/s)
4. A mass m is sliding down a slope of angle θ with no friction.
a) write a force equation
(F N=mgcos(θ); mgsin(θ)=ma)
b) find an expression for the acceleration.
(gsin(θ))
5. How long does it take a 20.0 kg mass to slide down a 13.0 m long, frictionless
ramp inclined at 8.50° ?
(4.24 sec)
6. A skater slides down an icy straight ramp. The ramp is 8 metres long, and it
takes the skater 5.6 seconds to move down the ramp (assume frictionless). Find
the angle of the ramp.
(3°)
7. A mass m is sliding down a slope of angle θ with friction coefficient µk .
a) write a force equation using these variables
b) find an expression for the acceleration.
(F N=mgcos(θ); mgsin(θ)-µFN =ma ; a=gsin(θ) - µk g cos(θ))
8. A 10. kg mass slides up a 30.° incline with an initial speed of 10. m/s. The
incline has friction coefficient µk =0.15. Find
a) force equations b) Ff & direction
b) acc'n
c) time to stop
( F N=mgcos(θ); mgsin(θ)+Ff =ma; 13 N down slope; 6.2 m/s2; 1.6 sec)
9. A 10 kg mass slides up a ramp inclined at 10.0° and stops after 4.06 metres. If
the mass was initially moving at 4.00 m/s, find the coefficient of friction.
(0.0278)
10. A mass m is sliding UP a slope of angle θ with friction coefficient µk .
a) write force equations
( F N=mgcos(θ); mgsin(θ)+ µFN =ma)
b) find an expression for the acceleration.
(a= gsin(θ) + µk g cos(θ)
Physics 12 Student Workbook
©Donald J. Mathewson 2002
117
11. A 5.0 kg mass is at rest on a 15° slope. Find the value of µs.
(0.27)
12. The friction of rubber soles on asphalt shingles is µs,max = 0.70. What is the
maximum angle roof at which a 55 kg roofer can walk without slipping? (35°)
13. A mass m is at rest on a slope of angle θ with friction coefficient µs.
a) write force equations
(F N=mgcos(θ); mgsin(θ)=Ff )
b) Find an expression for µs.
(µs= tan(θ) )
14. The table below has leg separation L= 1.25 metres. A textbook placed on it
starts to slide when the table is lifted to a height of H= 45.0 cm. Find the friction
coefficient between the book and table.
(0.386)
L
H
15. A 2.2 kg mass moving at 20.0 m/s starts up a 25.0° slope that has µk =0.150. It
slows down, stops, and then remains held in place by static friction. Find
a) how far it slides
b) µs
(36.5 m; 0.466)
16. If the mass shown below is to remain stationary, then find
a) the maximum value of F
b) the minimum value of F
(1660 N; 416 N)
150. kg
F
45.0°
µ
-s-max=0.600
(hint: if F is large, which way would the mass tend to slide? and so what will be
the direction of friction?)
Physics 12 Student Workbook
©Donald J. Mathewson 2002
118
Unit 2 Lesson 7
Exercises
1. For the system below, find
a) direction of motion
b) friction & direction
c) acc'n
d) cord tension
(4.0 kg goes up, 10. kg slides down)
(7.51 N up ramp)
(1.16m/s2)
(43.8 N)
mu-k=0.100
mu-s-max=0.100
4.00
kg
10.0 kg
40.0°
2. A cart is given a push, so that it travels up a frictionless ramp. The cart slows
to a stop and then rolls back down the ramp. What can be said about the
acceleration of the cart as it is going up the ramp and as it is going down?
A) the acceleration is greater when the cart is going up
B) the acceleration is greater when the cart is going down
C) the acceleration is the same when the cart is going up and down
rises
falls
push
3. In the diagram below, the surfaces are frictionless and the system is at rest.
How large is the mass M?
(7.66 kg)
5.00 kg
M
30.0°
Physics 12 Student Workbook
©Donald J. Mathewson 2002
50.0°
122
4. The system shown is at rest, but if pushed slightly, it will begin sliding.
Find a) friction force
b) direction system will move
c) coefficient of maximum static friction
(4.90 N; 3kg down; 0.115)
5.00 kg
3.00
kg
30.0°
5. Find the direction of motion and the acceleration
µ=0
10. kg
120 N
32°
(up ramp; 5.0m/s2)
6. If the surface shown below is frictionless and the system moves at constant
speed, find the value of θ.
(58°)
6.0 kg
5.0 kg
θ
45°
7. A mass is initially sliding down a rough (µ=0.700) 8.00° ramp at 2.50 m/s. How
far does it slide before stopping?
(0.576 m)
Physics 12 Student Workbook
©Donald J. Mathewson 2002
123
8. For the system below, find
a) direction of motion
b) acceleration
c) speed of system after 3 seconds
(to right; 0.197 m/s2, 0.592 m/s)
mu=0.100
5.00 kg
6.00 kg
45.0°
40.0°
9. A 50.0kg water skier initially moving at 18.0 m/s slides up a 7.00m long
frictionless ramp inclined at 30.0°. Find
a) acc'n on ramp
b) speed when leaving ramp
c) height of ramp at end
d) flight time of skier
e) range of skier
(4.90 m/s2; 16.0 m/s; 3.50 m; 1.99 sec; 27.5 m)
v=?
18.0 m/s
30°
30.0°
10. A 50. kg box is on a truck that is moving East at 15 m/s î. The truck slows
quickly to a stop, accelerating at (-6.2 î) m/s2. The box remains at rest on the
back of the truck, but just barely.
a) discuss the direction of the friction force on the box
b) write force equations for the box (Ff =ma)
c) find the coefficient of friction between the box and the truck. (0.63)
box
15 m/s
box
truck
truck
rest
11. Draw force diagrams for each of the masses and write force equations
upwards acc'n
m1
m2
(T1-m 1g-T 2=m1a T2-m 2g = m2a)
Physics 12 Student Workbook
©Donald J. Mathewson 2002
124
Unit 2 Lesson 8
Exercises
1. A 25.0 kg lawn mower is pushed with 500. N of force. The handle angle is
45.0° and the friction coefficient is µk =0.150. Find the acceleration (10.6 m/s2)
2. A 50.0 kg mower is PULLED with a 300. N force along its handle, which is at
40.0°. If µk =0.100, find the normal force, friction force and acceleration
(297 N, 29.7 N, 4.00 m/s2)
3. Find the normal force, the friction force and the acceleration for this
system.
(87.7 N, 8.77 N, 1.44 m/s2)
12.0 N
8.00 kg
15.0°
µ=0.100
4. Which direction will this system move?
(down the ramp)
60.0 N
30.0°
20.0 kg
30.0°
5. In #4, assume that µk =0.100 and find the normal force, net force down the
ramp and the acceleration (200. N; 26.1 N; 1.30 m/s2)
6. If the boat shown below goes straight East then find the force F and the
acceleration
(150. N, 2.60 m/s2)
F
100. kg
300. N
30.0° S of E
7. Linda pulls on a sled with a force of 89.00 N at 30.0° E of N. Elaine pulls with
66.75 N at 5.00° W of N. Find the resultant force & direction (149 N, 15.0° EofN)
8. Find the net force & direction by adding the two force vectors graphically
F1 = 30.0 N East
F2 = 45.0 N at 20.0° E of N (62.0 N, 43.0° N of E)
Physics 12 Student Workbook
129
©Donald J. Mathewson 2002
9. Find the net force (and direction) in each case
4.0 N
4N
4.0 N
3N
4N
3.0 N
3.0 N
4N
4.0 N
2.0 N
7N
4.0 N
10. N
5.0 N
2.0 N
7N
3N
7N
5.0 N
7N
7N
7N
(0N, 1 N East, 5.0 N 53°N of E,
5.0 N 37°S of W, 5.0 N 53° N of E,
5.0 N 37°S of W, 10 N NE,
10 N NE, 0 N, 7 N S)
10 N, SW
10 N, SW
10. Find the tension in the two strings if the mass is at rest (30.4 N; 7.90 N)
15.0°
3.00 kg
11. Find the cord tension (note since the angles are the same, the tension will
be the same in both cords)
(115 N)
20.0 °
20.0°
8.00 kg
12. If in question 11, we make both of the angles smaller, what will happen to
the tension?
a) increase
b) decrease
c) remain the same
Using principles of physics, explain your answer
Physics 12 Student Workbook
©Donald J. Mathewson 2002
130
Unit 2 Lesson 9
Exercises and Review
1. a) write force equations
b) find the tension in the two cords supporting the load
20.0 °
60.0°
20.0 kg
(187 N; 99.5 N)
2. Two force scales are set up as shown below and they measure 40 N of tension
in the cord. If another force scale is then attached and we exert 10 N of
sideways force on the cord, then which of the following could be the readings
on the force scales at the end of the cord?
Note that the cord has been deflected by a very small angle (< 5°)
a) 45 N
b) 41 N
c) 40 N
d) 50 N
e) more than 50 N
scale
scale
40 N
40 N
scale
scale
?
?
scale 10 N
Using principles of physics explain your answer.
3. A wedge is an inclined plane that can be used to amplify forces. Consider the
wedge below which is begin pushed downwards and is in equilibrium.
Find the normal force on the sides of the wedge (ignore friction and the mass
of the wedge)
120. N
120. N
axe
FN
10.0°
FN
block of wood
(688 N)
4. Find the force required to maintain equilibrium if a 20.0 N force acts east
and a 40.0 N force acts South
(44.7 N; 63.4° N of W)
Physics 12 Student Workbook
©Donald J. Mathewson 2002
135
5. Draw a force diagram and write net force equations
θ
a)
static
static
1
b)
2
θ
static
static
θ
φ
1
e)
θ
d)
falling
no air resistance
c)
static
f)
2
static
frictionless
frictionless
h)
g)
θ
θ
static
i)
rough
j)
θ
sliding at constant speed
frictionless
sliding right and slowing down
k)
l)
rough
accelerating up
Physics 12 Student Workbook
©Donald J. Mathewson 2002
136
n)
m)
accelerating down
accelerating
right
θ
a) T1sin(θ) = mg; T1cos(θ) = T2
b) T=mg
c) mg = ma
d)Tcos(θ)=T cos(θ) ; 2T sin(θ) = mg
e) T1cos(θ) = T2cos(φ) ; T1sin(θ) + T2sin(φ) = mg
f) FN=mg
g) F N=mgcos(θ); T=mgsin(θ)
h) mgsin(θ) = ma
i) F N=mgcos(θ); Ff =mgsin(θ)
j) F N=mg
k) FN - mg = ma
l) F N=mg; Ff = ma
m) mg- T = ma
n) T sin(θ) = mg; T cos(θ) = ma)
7. If a railcar (with pendulum) is given an initial velocity so that it moves up a
frictionless ramp a certain distance before stopping, which diagram shows the
correct position of the pendulum as the cart is rising up the ramp
a)
b)
c)
d)
Using principles of physics explain your answer.
8. Solve for the tension in the cords using graphical addition of vectors
55.0 °
cable 1
cable 2
50.0 kg
(598 N; 343 N)
9. A 1200. kg rocket car is placed at the bottom of a 100. metre long ramp
inclined at 10.0°. The rocket is turned on and it exerts a force of 8300 N for 5.70
seconds, and then it shuts down. Find the speed with which the rocket car
leaves the ramp (assume frictionless)
(28.8 m/s)
10. An object moves for 2.00 hours at 120. kph NorthEast, then travels 220. km
at 30.0° S of E at a constant 80.0kph, then moves at 100. kph for a distance of
75.0 km to the West. Find
^
a) the displacement vector
(285î + 59.7j
= 291 km, 11.8°NE)
b) the average velocity vector
(53.0 kph, 11.8° N of E)
c) the average speed
(97.3 kph)
Physics 12 Student Workbook
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137
Lesson 10: Practice Exam
Section I. Multiple Choice.
1 mark each, 30 marks total
1) A 15 kg block rests on a level, frictionless surface and is attached via a
string and pulley to a 5.0 kg overhanging mass. The system is released. Find
the tension in the string
a) 65 N b) 17 N c) 49 N d) 37 N e) 24.5 N
15 kg
5 kg
2) A 2.00 kg block is placed on a frictionless incline of 40.0°. What is the
acceleration once the mass is released? a= _____ m/s2
a) 7.50 b) 3.14 c) 6.30 d) 12.6 e) 0
3) Two forces act on a 35 kg object: a 30. N force due North and a 40. N force due
East. What is the acceleration of the object? a=_____m/s2
a) 1.4 b) 155 c) 3.5 d) 0.7
e) 2
4) A mass m is placed on a frictionless 30.° incline. If the incline is 10. metres
long, how long does it take the mass to reach the bottom?
a) 1.5 s b) 1.4 s c) 4.1 s d) 2.4 s e) 2.0 s
5) A 2000. kg sailboat experiences two forces: 3.0 × 103 N towards the East and
6.0 × 103 N towards the NorthWest. What is the direction of the acceleration?
a) 60.° N of W b) 30.° N of W c) 30.° N of E d) 74° N of W e) 52° N of W
6) A 5.00 kg block is moving upwards along a 30.0° incline with µk = 0.400. What
is its acceleration? a = ____________m/s2
a) 4.90 b) 1.51 c) 9.80 d) 3.39 e) 8.29
7) A person pushes a 20.0 kg lawnmower with a 100. N force along a 30.0°
handle. What is the normal force acting on the mower?
a) 98.0 N b) 198 N c) 196 N d) 246 N e) 282 N
30.0°
20.0 kg
8) What is the acceleration of the following Atwood machine? a=_____m/s2
a) 4.2
b) 3.0
c) 2.8
d) 9.8
e) 7.0
5.0 kg
2.0 kg
Physics 12 Student Workbook
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138
9) This system is at rest. How much friction is there on the incline mass and in
what direction does friction act? (up or down the ramp)
4 kg
3 kg
40°
a
b
c
d
e
friction
10 N
4N
4N
0.4 N
0.4 N
direction
up
down
up
up
down
****10 and 11*******************
A 250 kg crate rests on a level surface with µk = 0.12.
10) If a horizontal force of 7.5 × 102 N is needed to overcome the static friction
on a 250. kg crate, what is µs,max ?
a) 3.0 b) 0.15 c) 0.28 d) 0.31 e) 1.0
11) If the object begins to slide under a 750.1 N force, what is the acceleration
of the block? a= ______m/s2
a) 2.5 b) 1.8 c) 3.0 d) 3.8 e) 0
12) A soccer player kicks a 0.40 kg ball from rest to 9.0 m/s in 0.15 s. What is
the average force exerted on the ball?
a) 48 N b) 72 N c) 24 N d) 60 N
****13 and 14*************************
A hockey puck initially moving at 8.0 m/s travels across rough ice and stops in
16 m.
13) Find the acceleration of the puck: a= - ___________ m/s2
a) 1.0 b) 2.0 c) 2.4 d) 3.2 e) 0.5
14) What is µk ?
a) 0.05 b) 0.10 c) 0.20 d) 0.080 e) 0.25
****15 and 16************************
A 300. kg crate rests on an adjustable inclined plane.
15) If the crate starts to slide when the angle of the incline is 25°, what is the
maximum coefficient of static friction?
a) 0.42 b) 0.47 c) 0.90 d) 0.12 e) 2.14
Physics 12 Student Workbook
©Donald J. Mathewson 2002
139
16) If the incline is oiled so that an incline of 25° produces an acceleration of
0.70 m/s2 then what is the coefficient of kinetic friction?
a) 0.47 b) 0.42 c) 0.32 d) 0.12 e) 0.39
****17 and 18*************************
An elevator weighing 2.00 × 104 N is supported by a cable. The maximum
tension the cable can support is 3.00 × 104 N.
17) What is the cable tension if the elevator accelerates upwards at 3.00 m/s2?
a) 1.39 × 104 N b) 2.31 × 104 N c) 2.00 × 104 N d) 2.61 × 104 N e) 3.00 × 104 N
18) What is the maximum safe acceleration of the elevator?
a) 3.50 b) 2.50 c) 4.90 d) 0.500 e) 7.50
a=____ m/s2
19) You are in an elevator accelerating downwards at 1.0 m/s2. If your mass is
100. kg, what is your apparent weight?
a) 980 N b) 880 N c) 970 N d) 1080N e) 100 N
20) A skydiver is falling through the air. If he adjusts his parachute so that
the force of air resistance from his chute balances the force of gravity, what
will happen?
a) he will stop b) he will slow down c) he will fall at constant velocity
d) the chute will break e) he will continue to speed up
21. A car accelerates from rest up a hill. Which is the best force diagram?
Note that the car is rolling and not sliding.
A
C
B
D
22. Select the best response:
In order to start an object moving on a rough surface, ____________________
a) you must have maximum static friction
b) you pull with a force slightly larger than the force of kinetic friction
c) the force you pull with must exceed the force of friction
d) your maximum force must pull with more friction
e) the applied force must be larger than maximum static friction
Physics 12 Student Workbook
©Donald J. Mathewson 2002
140
*********23, 24 and 25**********
Consider the two masses m1 and m2 which are supported by strings
string 1
m1
string 2
m2
23. What forces act on mass m1?
a) gravity , applied force, tension
b) upwards tension, applied force , gravity
c) upwards tension , downwards tension, net force
d) downwards tension , upwards tension, applied force
e) downwards tension, upwards tension, gravity
24. What is the tension in string 1 if the system is at rest? T = ______
a) weight of m1
b) weight of m1 and m2
c) weight of m2
d) zero
e) 9.8 N
25. If string 1 is cut and the two masses free-fall, what will be the tension in
string 2?
a) zero
b) weight of m1 and m2
c) weight of m2 only
d) weight of m1 only
e) 9.8
26. What is the net force on this mass?
6.0 N
8.0 N
a) 2.0 N
b) 14 N
c) 7.0 N
d) 10. N
e) 20. N
27. A mass M sits on a flat surface. If the surface is accelerating upwards,
which equation is true?
a) F = ma
b) T - mg = ma
c) mg = ma
d) T - Ff = ma
e) FN - mg = ma
Physics 12 Student Workbook
©Donald J. Mathewson 2002
141
28. What is the angle of a ramp if a rollerblader rolls from rest 6.0 metres in 2.5
seconds?
a) 29°
b) 14°
c) 11°
d) 5.6°
e) 1.9°
*******29 and 30 ******************
2.0 kg
frictionless
3.0 kg
7.0 kg
a = _________m/s2
29. What is the acceleration of this system ?
a) 3.9
b) 3.3 c) 5.7 d) 2.5 e) 2.0
30. What is the correct force diagram (arrows to scale) for the 2 kg mass?
A
D
C
B
1
d
2
c
3
a
4
e
5
d
6
e
7
d
8
a
9
b
10
d
11
b
12
c
13
b
14
c
15
b
16
e
17
d
18
c
19
b
20
c
21
a
22
e
23
e
24
b
25
a
26
d
27
e
28
c
29
b
30
c
Section II: Problems.
Answer in the space provided. (20 marks total)
1. (5 marks) A 3 kg object is placed on a 35° incline where µ = 0.25 and then
released. Write force equations and find the acceleration. (3.6 m/s2)
2. (5 marks) A student of mass M puts a bathroom scale on a skateboard and
then rolls down a ramp which in inclined at angle θ. What will the scale read?
a) M
b) less than M
c) more than M
Using principles of physics explain your answer.
explanation: _________________________________________________________
_________________________________________________________
Physics 12 Student Workbook
©Donald J. Mathewson 2002
142
3. (5 marks) A person holds a book against a wall by pushing on an 50.0° angle
as shown below with a force of 27.0 N. The friction constant for the book on
the wall is µ=0.220. The book is barely held in place by the 27.0 N force, ie it is
tending to fall.
a) draw a force diagram for the book; clearly label all forces acting on it
b) write vertical and horizontal force equations
c) find the book mass
bonus) find the maximum force the person could exert on this book (at the
angle shown below) and still have it remain at rest.
vertical
book
50°
horizontal
push
wall
(F sin(50) = FN; F cos(50) + Ff = mg ; 2.24 kg; 46.2 N)
4. (5 marks) An object on an incline is acted upon by a horizontal force F. If
the friction coefficient is µ, write the force equations for the system.
F
θ
θ
(F sin(θ) + mg cos(θ) =FN ; F cos(θ) -F f - mgsin(θ) = ma
OR
mgsin(θ) -F cos(θ) -F f - = ma )
Physics 12 Student Workbook
©Donald J. Mathewson 2002
143
other (hard) practice exam problems
1. What is the minimum force F required to keep the mass at rest on the incline
if the coefficient of friction is µ = 0.270? The force is perpendicular to the
incline and the mass is 10.0 kg.
F
10.0 kg
20.0°
(32.0 N)
2. A 10.0 kg object on an 32.0° incline is acted upon by a horizontal force (F). If
the friction coefficient is µ = 0.150, find the maximum and minimum force for
which the object will not move.
F
32°
32°
(83.8 N; 42.5 N)
3. Find the smallest value of the mass M for which the system will remain at
rest given that the coefficient of static friction is 0.100
15.0 kg
µ=0.100
M
25.0°
Physics 12 Student Workbook
©Donald J. Mathewson 2002
(4.98 kg)
144
4. Find the tension in the cord connecting the 6.00 kg and 2.00 kg masses.
Assume all surfaces are frictionless.
(1.96 N)
2.00 kg
6.00 kg
10°
5.00 kg
40°
5. A person holds a 6.00 kg book against a wall by pushing on an 50.0° angle as
shown below. The friction constant for the book on the wall is µ=0.220
a) draw a force diagram for the book
b) write vertical and horizontal force equations
c) find the minimum push force required to keep the book at rest.
bonus) why does the word 'minimum' need to be specified in this problem?
Your answer should include a calculation (its up to you to decide what to
calculate)
vertical
6 kg book
horizontal
50°
wall
push
(F sin(50) = FN; F cos(50) + Ff = mg ;72.5 N ; at rest for any force 72.5 N to 124 N)
6. For the system below, find the maximum and minimum value of the mass M
for which the system will remain at rest.
30.0°
mu-s-max=0.300
mu-k=0.200
M
10.0 kg
20.0°
Physics 12 Student Workbook
©Donald J. Mathewson 2002
(16.3 kg; 119 kg)
145