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Phys 110
1- The Young modulus of a certain material is given by  
FL0
where F is the force, L0 is the initial
AL
length, L is the difference in length, and A is the area. The unit of the modulus is:
(a) N.m
(b) N
(c) N/m
(d) kg/(m.s)
(f) kg.m/s
2- The force acting on a moving object is given by F= bvt where v is the speed and t is time. The SI unit
of the constant b is:
(a) kg.s2
(b) kg/s2
(c) kg.m/s2
(d) kg.s2/m
(f) kg.m/s
3- The magnitude of the force acting on a particle is 5.6×107 dyne where1 dyne=1 g.cm/s2. The
magnitude of the force in SI system is:
(a) 5.6×102
(b) 5.6×104
(c) 5.6×105
(d) 5.6×109
(f) 5.6×1012
4- The density of a certain substance is 13.6 g/cm3. The density of the substance in SI units is:
(a) 13.6×102
(b) 13.6×103
(c) 13.6×104
(d) 13.6×105
(f) 13.6×106
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

5- Three vectors A  2  x iˆ  ˆj  3kˆ , B  iˆ  2 ˆj  kˆ , and C  5 ˆj  2kˆ where A is normal to
B  3C  . The value of x is:
(a) 2
(b) 4
(c) 0

(d) -2


(f) -4
  
6- Having two vectors A  2iˆ  3 ˆj and B  iˆ  2 ˆj  kˆ , the result of A  B  A is:
(a) iˆ  ˆj
(b) 1
(d) iˆ  ˆj
(c) 0



(f) -4

7- Considering the vectors N  4iˆ  6kˆ and M  3 iˆ  2 ˆj  2kˆ , the vector normal to both is:
(a) 36iˆ  10 ˆj  24kˆ
(b) 36iˆ  10 ˆj  20kˆ
(c) 18iˆ  5 ˆj  12kˆ
8- In the previous question, the angle between the two vectors is:
(a) 61.6
(b) 30
(c) 48.9
(d) 36iˆ
(f) 36iˆ  2 ˆj
(d) 0
(f) 54.3
9- A vector, having a magnitude of 5 units and lying on xy-plane, is normal to 3iˆ  6 ˆj  2kˆ . The
unknown vector is:
(a)
5iˆ  ˆj
(b)  2 5iˆ  5 ˆj
(c)  2iˆ  5 ˆj

(d) 2 5iˆ  5 ˆj
(f) 2iˆ  ˆj

10- Two vectors have magnitudes of A  5 and B  6 . If the magnitude of their resultant vector
 
A  B is 9, their scalar product is:
(a) 0
(b) 5
(c) 10

(d) 15
(f) 20

11- Two vectors have magnitudes of A  8 and B  12 . If the magnitude of their resultant vector
 
 
A  B is 15, the value of A  B is:
(a) 12.52
(b) 13.82
(c) 14.61
(d) 15.25
(f) 16.03
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




12- For two vectors, A and B , A  B  5 units and A  B  3 units. If the magnitude of the vector


B is 2 units, the magnitude of vector A is:
(a) 2.6
(b) 3.6
(c) 4.6


 

(d) 5.6
(f) 6.6

13- For non-zero vectors A and B , A  B  A  B . The angle between the two vectors is:
(a) 0
(b) 30
(c) 45

(d) 60
(f) 90

14- Having known that A  2  x iˆ  ˆj  3kˆ and B  iˆ  2 ˆj  kˆ are perpendicular, the value of x is:
(a) 3
(b) 5
(c) 7
(d)9
(f) 0


  


15- Three vectors are a  3iˆ  4 ˆj  kˆ , b  2iˆ  3kˆ , and c  2 ˆj . The result of a.b c is:


(a) c  6 ˆj

(c) c  6 ˆj  3kˆ (d) 6iˆ
(b) c  6 ˆj

(f) 6



 

16- If a  iˆ  ˆj and b  iˆ  ˆj , the vector ka  b being parallel to c  3iˆ  ˆj if the value of k is:
(a) -0.25
(b) -0.5
(c) 0
(d) 0.25
(f) 0.5




17- A and B are two vectors in xy plane. If A  2iˆ  4 ˆj and the x-component of B is2.5, the y-



component of B that makes A and B perpendicular is:
(a) 1.0
(b) 1.25
(c) 1.5
(d) 2.0

(f) 2.5

18- The position of a particle at any time is given as xt   2 t  3  5t , where x is measured by meters
and t in seconds . The initial speed of the particle is:
(a) 6 m/s
(b) 5 m/s
(c) 4 m/s
(d) 3 m/s
(f) 2 m/s
3
19- In the previous question, the acceleration of the particle at t  2 s is:
(a) 6 m/s2
(b) 12 m/s2
(c) 18 m/s2
(d) 24 m/s2

(f) 36 m/s2

20- A body, initially at the origin, moves with a velocity given by vt   t t  1 m/s. The average
velocity of the body between t=2 s and t=3 s is:
(a) 13.75 m/s
(b) 10.26 m/s
(c) 6.75 m/s
(d) 3.51 m/s
(f) 30 m/s
2
21- The position of a ball thrown vertically upwards is given by the equation y = 1.00 + 25.0t –5.0t2 (SI
units), the average velocity for the first 2.0 s is:
(a) 5 m/s
(b) 10 m/s
(c) 15 m/s
(d) 20 m/s
(f) 25 m/s
22- A car moves with constant speed of 24 m/s. If the driver applies breaks to completely stop the car in
the front of 120 m away pedestrian, it will take:
(a) 2 s
(b) 4 s
(c) 6 s
(d) 8 s
(f) 10 s
23- A car covers 37.5 m in 5 s to increase its speed to 12 m/s. The initial speed of the car is:
(a) 3 m/s
(b) 5 m/s
(c) 7 m/s
(d) 9 m/s
(f) 11 m/s
24- A bicycle starts its motion from rest and accelerates to 8 m/s in 40 m. The magnitude of its
acceleration is:
(a) 0.6 m/s2
(b) 0.8 m/s2
(c) 1.0 m/s2
(d) 1.2 m/s2
(f) 1.4 m/s2
25- A ball is thrown vertically upward with initial speed of 9.8 m/s, its maximum height is:
(a) 9.8 m
(b) 19.6 m
(c) 4.9 m
(d) 39.2 m
(f) 20 m
26- A stone is freely dropped from 39.2 m above the ground, its speed at the midway is:
(a) 9.8 m/s
(b) 19.6 m/s
(c) 4.9 m/s
(d) 39.2 m/s
(f) 20 m/s
27- A stone is thrown directly upwards with an initial speed of 5.0m/s, from some unknown height
above the ground. If the stone strikes ground 2.50s later, the height at which the stone was thrown is:
(a) 12.8 m
(b) 14.1 m
(c) 15.9 m
(d) 18.1 m
(f) 19.6 m
28. A ball is thrown vertically upward with 20 m/s, the magnitude of its acceleration after 1.2 s is:
(a) 9.8 m/s2
(b) 3.6 m/s2
(c) 2.8 m/s2
(d) 1.4 m/s2
(f) 0 m/s2
29. A ball is thrown vertically upwards. If the ball is caught at 4.0 m above the ground after 1.5 s, the
initial speed of the ball is:
(a) 10.02 m/s
(b) 9.8m/s
(c) 6.8 m/s
(d) 3.8 m/s
(f) 19.6 m/s
30. A red ball is thrown vertically upwards with 20 m/s. One second later, a blueball is thrown upwards
by 30 m/s. Both balls will meet at a height of (above the ground):
(a) 39.2 m
(b) 25.5 m
(c) 15.9 m
(d) 18.1 m
(f) 19.6 m
31. A ball is thrown vertically upward with initial speed v0. If the position of the ball at a certain time is
given by y = 19.6t–4.9t2, the initial speed of the ball is:
(a) 4.9 m/s
(b) 9.8m/s
(c) 19.6 m/s
(d) 39.2 m/s
(f) 0 m/s
32- An object is thrown vertically upwards. Taking the upwards direction as the positive, the velocity
and acceleration of the object at the maximum height are:
(a) 0,0
(b) +gt,0
(c) –gt,0
(d) 0,-g
(f) 0,+g
Problems
1. Calculate:
a. the weight of a 16-newton object in pounds
b. the weight of a 7-pound object in newtons
c. the weight of a 3-kilogram object on Earth in newtons
d. the mass in kilograms of an object that weighs 12 newtons on Earth
2. How does the inertia of a 200-kg object compare to the inertia of a 400-kg
object?
3. A constant force is applied to a cart, causing it to accelerate. If the mass of
the cart is tripled, what change occurs in the acceleration of the cart?
4. If the net force acting on an object is tripled, what happens to its
acceleration?
5. On the planet of Venus, the acceleration due to gravity is 8.86 m/s 2. What is
the mass of a man weighing 800 N on the surface of that planet?
6. A 60-kilogram boy rolls downhill on a bicycle with a mass of 12 kilograms.
What net force is acting on the boy and his bicycle if he accelerates at a rate
of 3.25 m/s2?
7. A young girl whose mass is 30 kilograms is standing motionless on a 2-kg
skateboard holding a 7-kg bowling ball. She throws the ball with an average
force of 75 N.
a. What is the magnitude of her acceleration?
b. What is the magnitude of the acceleration of the bowling ball?
8. On the planet Mercury, a person with a mass of 75 kg weighs 280 N. What
is the acceleration due to gravity on Mercury?
9. As a baseball player strikes the ball with his bat, the 1-kg bat applies an
average force of 500 N on the 0.15-kg baseball for 0.20 seconds.
a. What is the force applied by the baseball on the bat?
b. What is the acceleration of the baseball?
c. What is the speed of the baseball at the end of the 0.2 seconds?
10. The graph
represents the
motion of a
1500-kg car
over a 20second interval.
During which
interval(s) is the
net force on the
car zero?
11. Referring to the
graph, what
force is being
applied to the
car during
interval C-D?
12. Two forces are applied to a 2-kilogram block on a frictionless horizontal
surface as shown in the diagram. Calculate the acceleration of the block.
13. The graph to the right represents the
acceleration of an object as a function of the
force applied to the object. What is the mass of
the object?
14. A 50-kg woman wearing a seat belt is traveling
in a car that is moving with a velocity of
10 m/s. In an emergency, the car is brought to
rest in 0.50 seconds. What force does the seat
belt exert on the woman so that she remains in
her seat?
Calculate the weight of each of the following:
a. A 60-kg person on Earth.
b. A 4-kg cat on Earth.
c. A 30-kg dog on Jupiter.
2. Calculate the mass of each of the following:
a. A car that weighs 15,000 N on Earth.
b. A frog that weighs 12 N on Jupiter.
3. Chris has a mass of 75 kg. He stands on a scale in an elevator that is
accelerating downward at 4.9 m/sec2. What force does the scale display in
newtons?
4. Calculate the static friction between your sneakers (rubber) and the
sidewalk (concrete) if your mass is 55 kg.
5. While vacuuming, you pull the sofa away from the wall. The sofa weighs
500 N, and the force of sliding friction between the sofa and the carpet is
200 N. Calculate the coefficient of sliding friction between the sofa and the
carpet.
6. While ice skating, you push off of a wall with a force of 100 N. Calculate
your acceleration if you have a mass of 50 kg and the coefficient of sliding
friction between your skates and the ice is 0.10.
7. Draw the free-body diagram for each object:
a. A 1-kg rock sitting on a table.
b. A 500-N box at rest that you are pushing on with a force of 100 N.
c. A 20-kg monkey hanging from a tree limb by both arms.
8. Two children are fighting over a toy. While holding onto the toy, Toni
applies a force of 15 N to the right. Marie applies a force of 20 N to the left.
The mass of the toy is 2.5 kg. Calculate the acceleration of the toy.
9. Calculate the size of the restoring force in each scenario:
a. A spring with a spring constant of 20 N/m is stretched 0.5 m.
b. A spring with a spring constant of 3 N/m is compressed 0.1 m.
c. A wall with a spring constant of 5 x 10 7 N/m is compressed
1 10-5 m.
1. Explain the difference between scalar and vector quantities.
2. Classify each of the following as a scalar or vector:
a. height
b. displacement
c. velocity
d. area
3. Draw a vector to show a displacement of 100 meters at an angle of 30
degrees. Use a scale for your drawing.
4. You walk 1 kilometer north to the store, turn around, and return home. What
is your displacement?
5. What is the maximum resultant of a 1 centimeter vector and a 4 centimeter
vector? What is the minimum resultant?
6. Vectors can be expressed using Cartesian coordinates and polar coordinates.
What type of quantity is each coordinate when a vector is expressed using
Cartesian coordinates? What type of quantity is each coordinate when a
vector is expressed using polar coordinates?
7. If a vector is at 45 degrees, what do you know about the magnitude of its
components?
8. List three advantages of using components rather than a scale drawing to
add a set of vectors.
9. What is the only force that affects the motion of a projectile?
10. Which component of a projectile’s velocity changes as it moves through the
air, the horizontal component or the vertical component?
11. A ball rolls off the edge of a horizontal table. What is the initial vertical
velocity component?
12. A soccer ball is kicked off the ground at an angle of 45 degrees.
a. At the top of its path, is its velocity entirely horizontal, entirely
vertical, or a combination of both? Explain your reasoning.
b. At the top of its path, is its acceleration entirely horizontal, entirely
vertical, or a combination of both? Explain your answer.
13. At what angle should a ball be thrown for it to travel a maximum distance?
14. A ball kicked at an angle of 25 degrees will have the same range as a ball
kicked at the same speed at ___ degrees.
15. What does it mean for an object to be in equilibrium?
16. Give three examples of objects moving along an inclined plane.
17. A sled is sliding down an icy hill.
a. List the three forces that act on the sled as it
moves down the hill.
b. Draw a diagram to show the direction of each of
the forces on the sled.
18. Which force acting on an object on an inclined plane
causes it to accelerate?
19. Which force acting on an object on an inclined plane decreases its
acceleration?
20. If an object is in equilibrium, what is the net force in the x-direction? In the
y-direction?
Problems
1. Add the following sets of vectors. N = north, W = west, and S = south.
a. 2 cm N + 7 cm W
b. 5 m S + 8 cm N
c. 30 m/s W + 50 m/s S
d. 5 cm N + 7 cm W + 9 cm S
2. Resolve the vector (6 cm, 25 degrees) into x-y components.
3. Calculate the components of the vector representing a velocity of 40 meters
per second at an angle of 55 degrees.
4. A pilot wants to fly directly to the west. The engine pushes the plane at 100
m/s, and there is a crosswind blowing to the south at 30 m/s. Determine the
exact angle at which the pilot should head.
5. You and a friend are rowing a boat. You aim it toward a dock directly across
the 100 meter-wide river and paddle at a speed of 1 m/s. You both are
concentrating on rowing, so you do not notice that there is a 2 m/s current
pushing you downstream. How far from the dock will you be when you
reach the shore? Will the time it takes to cross the river be affected by the
current?
6. You take a running jump off the end of a diving platform at a speed of 7 m/
s and splash into the water 1.5 seconds later.
a. How far horizontally do you land from your takeoff point?
b. How high is the diving platform?
7. A model rocket is launched into the air so that its initial horizontal speed is
20 m/s and its initial vertical speed is 39.2 m/s. Complete the chart by
finding the horizontal and vertical components of the velocity each second.
8. A circus performer wants to land in a net 5 meters to the right of where she
will let go of the trapeze. If she is 10 meters above the net, how fast must
she be moving horizontally when she lets go?
9. You hit a baseball at a speed of 35 m/s and an angle of 40 degrees. A player
catches the ball at the same height off the ground as the hit.
a. Find the horizontal and vertical components of the ball’s initial
velocity.
b. How many seconds will the ball take to get to the top of its path?
c. How much time will the ball spend in the air?
d. How far off the ground will the ball be at its highest point?
e. How far horizontally will the ball travel?
10. A swing is designed so the ropes hang at an angle of 10 degrees from the
vertical. A child with a weight of 200 newtons sits on the swing.
a. How much tension is in each rope?
b. How does the tension compare with the tension in a swing with ropes
that are completely vertical?
11. Chris rides a sled down a hill with a slope of 22 degrees. The combined
weight of Chris and his sled is 500 newtons.
a. What is the normal force of the ground on the sled?
b. Calculate the component of the weight that is parallel to the ground.
c. Assuming the ground is frictionless, what is Chris’s acceleration?
d. If Chris’s little sister also rides on the sled, their combined weight is
700 newtons. What is the new acceleration?
e. Compare your answers to parts c and d. Can you explain this?
12. A 2 kilogram object slides down a frictionless slope.
a. Calculate its acceleration if the slope is angled at 30 degrees.
b. Calculate its acceleration if the slope is angled at 60 degrees.
c. Compare your answers to parts a and b. Can you explain this?
13. A heavy cardboard box full of books slides down a wooden inclined plane
with a certain acceleration. Identify whether each suggested change would
result in an increased acceleration, decreased acceleration, or no change in
the acceleration.
a. greasing the inclined plane to lower the coefficient of sliding friction
b. adding more books to the box
c. decreasing the angle of the inclined plane