Deck 6: Force and Motion II

Question 1

A 24-N horizontal force is applied to a 40-N block initially at rest on a rough horizontal surface. If the coefficients of friction are $\mu$ _s = 0.5 and $\mu$ _k = 0.4, the magnitude of the frictional force on the block is:

A) 12 N
B) 16 N
C) 20 N
D) 24 N
E) 40 N

Answer 1

16 N

Question 2

A crate rests on a horizontal surface and a woman pulls on it with a 10-N force. No matter what the orientation of the force, the crate does not move. Rank the situations shown below according to the magnitude of the frictional force of the surface on the crate, least to greatest.

A) 1, 2, 3
B) 2, 1, 3
C) 2, 3, 1
D) 1, 3, 2
E) 3, 2, 1

Answer 2

3, 2, 1

Question 3

A forward horizontal force of 12 N is used to pull a 240-N crate at constant velocity across a horizontal floor. The coefficient of friction is:

A) 0.5
B) 0.05
C) 2
D) 0.2
E) 20

Answer 3

0.05

Question 4

A 400-N block is dragged along a horizontal surface by an applied force as shown. The coefficient of kinetic friction is u_k = 0.4 and the block moves at constant velocity. The magnitude of is:

A) 100 N
B) 150 N
C) 200 N
D) 290 N
E) 400 N

Question 5

A block of mass m is pulled along a rough horizontal floor by an applied force as shown. The vertical component of the force exerted on the block by the floor is:

A) mg
B) mg - T cos $\theta$
C) mg + T cos $\theta$
D) mg - T sin $\theta$
E) mg + T sin $\theta$

Question 6

A block of mass m is pulled at constant velocity along a rough horizontal floor by an applied force as shown. The magnitude of frictional force is:

A) T cos $\theta$
B) T sin $\theta$
C) 0
D) mg
E) mg cos $\theta$

Question 7

A horizontal shove of at least 200-N is required to start moving an 800-N crate initially at rest on a horizontal floor. The coefficient of static friction is:

A) 0.125
B) 0.25
C) 0.50
D) 4.00
E) none of these

Question 8

A car is traveling at 15 m/s on a horizontal road. The brakes are applied and the car skids to a stop in 4.0 s. The coefficient of kinetic friction between the tires and road is:

A) 0.38
B) 0.69
C) 0.76
D) 0.92
E) 3.75

Question 9

The coefficient of kinetic friction:

A) is in the direction of the frictional force
B) is in the direction of the normal force
C) is the ratio of force to area
D) can have units of newtons
E) none of the above

Question 10

A professor holds an eraser against a vertical chalkboard by pushing horizontally on it. She pushes with a force that is much greater than is required to hold the eraser. The force of friction exerted by the board on the eraser increases if she:

A) pushes with slightly greater force
B) pushes with slightly less force
C) stops pushing
D) pushes so her force is slightly downward but has the same magnitude
E) pushes so her force is slightly upward but has the same magnitude

Question 11

A box with a weight of 50 N rests on a horizontal surface. A person pulls horizontally on it with a force of 15 N and it does not move. To start it moving, a second person pulls vertically upward on the box. If the coefficient of static friction is 0.4, what is the smallest vertical force for which the box moves?

A) 5 N
B) 12 N
C) 20 N
D) 25 N
E) 35 N

Question 12

A boy pulls a wooden box along a rough horizontal floor at constant speed by means of a force as shown. In the diagram f is the magnitude of the force of friction, N is the magnitude of the normal force, and F_g is the magnitude of the force of gravity. Which of the following must be true?

A) P = f and N = F_g
B) P = f and N > F_g
C) P > f and N < F_g
D) P > f and N = F_g
E) none of these

Question 13

A 40-N crate rests on a rough horizontal floor. A 12-N horizontal force is then applied to it. If the coefficients of friction are $\mu$ _s = 0.5 and $\mu$ _k = 0.4, the magnitude of the frictional force on the crate is:

A) 8 N
B) 12 N
C) 16 N
D) 20 N
E) 40 N

Question 14

A bureau rests on a rough horizontal surface ( $\mu$ _s = 0.50, $\mu$ _k = 0.40). A constant horizontal force, just sufficient to start the bureau in motion, is then applied. The acceleration of the bureau is:

A) 0 m/s²
B) 0.98 m/s²
C) 3.9 m/s²
D) 4.9 m/s²
E) 8.8 m/s²

Question 15

A boy pulls a wooden box along a rough horizontal floor at constant speed by means of a force as shown. In the diagram f is the magnitude of the force of friction, N is the magnitude of the normal force, and F_g is the magnitude of the force of gravity. Which of the following must be true?

A) P = f and N = F_g
B) P = f and N > F_g
C) P > f and N < F_g
D) P > f and N = F_g
E) none of these

Question 16

A force (larger than the largest possible force of static friction) is applied to the left to an object moving to the right on a horizontal surface. Then:

A) the object must be moving at constant speed
B) and the friction force act in opposite directions
C) the object must be slowing down
D) the object must be speeding up
E) the object will come to rest and remain at rest

Question 17

A brick slides on a horizontal surface. Which of the following will increase the frictional force on it?

A) Putting a second brick on top
B) Decreasing the surface area of contact
C) Increasing the surface area of contact
D) Decreasing the mass of the brick
E) None of the above

Question 18

A 12-kg crate rests on a horizontal surface and a boy pulls on it with a force that is 30 $\degree$ below the horizontal. If the coefficient of static friction is 0.40, the minimum magnitude force he needs to start the crate moving is:

A) 44 N
B) 47 N
C) 54 N
D) 56 N
E) 71 N

Question 19

The speed of a 4.0-N hockey puck, sliding across a level ice surface, decreases at the rate of 0.61 m/s². The coefficient of kinetic friction between the puck and ice is:

A) 0.062
B) 0.25
C) 0.41
D) 0.62
E) 1.2

Question 20

When the brakes of an automobile are applied, the road exerts the greatest retarding force:

A) while the wheels are sliding
B) just before the wheels start to slide
C) when the automobile is going fastest
D) when the acceleration is least
E) at the instant when the speed begins to change

Question 21

Block A, with a mass of 10 kg, rests on a 35 $\degree$ incline. The coefficient of static friction is 0.40. An attached string is parallel to the incline and passes over a massless, frictionless pulley at the top. The largest mass m_B, attached to the dangling end, for which A remains at rest is:

A) 2.5 kg
B) 3.5 kg
C) 5.9 kg
D) 9.0 kg
E) 10.5 kg

Question 22

A horizontal force of 12 N pushes a 0.50-kg book against a vertical wall. The book is initially at rest. If $\mu$ _s = 0.60 and $\mu$ _k = 0.50, the acceleration of the book is:

A) 0 m/s²
B) 9.4 m/s²
C) 9.8 m/s²
D) 14.4 m/s²
E) 19.2 m/s²

Question 23

A block is first placed on its long side and then on its short side on the same inclined plane. The block slides down the plane on its short side but remains at rest on its long side. A possible explanation is:

A) the short side is smoother
B) the frictional force is less because the contact area is less
C) the center of gravity is higher in the second case
D) the normal force is less in the second case
E) the force of gravity is more nearly down the plane in the second case

Question 24

A 50-N force is applied to a crate on a horizontal rough floor, causing it to move horizontally. If the coefficient of kinetic friction is 0.50, in what direction should the force be applied to obtain the greatest acceleration?

A) Horizontal
B) 60 $\degree$ above the horizontal
C) 30 $\degree$ above the horizontal
D) 27 $\degree$ above the horizontal
E) 30 $\degree$ below the horizontal

Question 25

A box rests on a rough board 10 meters long. When one end of the board is slowly raised to a height of 6 meters above the other end, the box begins to slide. The coefficient of static friction is:

A) 0.8
B) 0.25
C) 0.4
D) 0.6
E) 0.75

Question 26

A block is placed on a rough wooden plane. It is found that when the plane is tilted 30 $\degree$ to the horizontal, the block will slide down at constant speed. The coefficient of kinetic friction of the block with the plane is:

A) 0.500
B) 0.577
C) 1.73
D) 0.866
E) 4.90

Question 27

Block A, with mass m_A, is initially at rest on a horizontal floor. Block B, with mass m_B, is initially at rest on the horizontal top surface of A. The coefficient of static friction between the two blocks is $\mu$ _s. Block A is pulled with a horizontal force. It begins to slide out from under B if the force is greater than:

A) m_Ag
B) m_Bg
C) $\mu$ _sm_Ag
D) $\mu$ _sm_Bg
E) $\mu$ _s ( m_A + m_B)g

Question 28

Block A, with a mass of 50 kg, rests on a horizontal table top. The coefficient of static friction is 0.40. A horizontal string is attached to A and passes over a massless, frictionless pulley as shown. The smallest mass m_B of block B, attached to the dangling end, that will start A moving when it is attached to the other end of the string is:

A) 20 kg
B) 30 kg
C) 40 kg
D) 50 kg
E) 70 kg

Question 29

The same heavy wooden block is dragged by a force along a rough steel plate, as shown below for two possible situations. The magnitude of the acceleration is the same for the two situations; do not assume that the magnitude of is the same. The magnitude of the frictional force in (ii), as compared with that in (i) is:

A) the same
B) greater
C) less
D) less for some angles and greater for others
E) can be less or greater, depending on the magnitude of the applied force.

Question 30

A 5.0-kg crate is on an incline that makes an angle of 30 $\degree$ with the horizontal. If the coefficient of static friction is 0.50, the minimum force that can be applied parallel to the plane to hold the crate at rest is:

A) 0 N
B) 3.3 N
C) 21 N
D) 25 N
E) 46 N

Question 31

A crate resting on a rough horizontal floor is to be moved horizontally. The coefficient of static friction is 0.40. To start the crate moving with the weakest possible applied force, in what direction should the force be applied?

A) Horizontal
B) 24 $\degree$ below the horizontal
C) 22 $\degree$ above the horizontal
D) 24 $\degree$ above the horizontal
E) 66 $\degree$ below the horizontal

Question 32

A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 30 $\degree$ with the horizontal, the force of friction is:

A) 0 N
B) 17 N
C) 20 N
D) 25 N
E) 49 N

Question 33

A horizontal force of 12 N pushes a 0.50-kg book against a vertical wall. The book is initially at rest. If the coefficients of friction are $\mu$ _s = 0.60 and $\mu$ _k = 0.50 which of the following is true?

A) The frictional force is 4.9 N
B) The frictional force is 7.2 N
C) The normal force is 4.9 N
D) The block will start moving and accelerate
E) If started moving downward, the block will accelerate

Question 34

A crate is sliding down an incline that is 35 $\degree$ above the horizontal. If the coefficient of kinetic friction is 0.40, the acceleration of the crate is:

A) 0 m/s²
B) 2.4 m/s²
C) 3.9 m/s²
D) 5.6 m/s²
E) 8.8 m/s²

Question 35

A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If $\mu$ _s = 0.60 and $\mu$ _k = 0.50, the frictional force after a period of time is:

A) 0 N
B) 2.5 N
C) 3.0 N
D) 4.0 N
E) 4.9 N

Question 36

Block A, with a mass of 10 kg, rests on a 35 $\degree$ incline. The coefficient of static friction is 0.40. An attached string is parallel to the incline and passes over a massless, frictionless pulley at the top. The largest mass m_B, of block B, attached to the dangling end, for which A begins to slide down the incline, is:

A) 2.5 kg
B) 3.5 kg
C) 5.9 kg
D) 9.0 kg
E) 10.5 kg

Question 37

A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 25 $\degree$ with the horizontal, the force of friction is:

A) 0 N
B) 20 N
C) 21 N
D) 22 N
E) 44 N

Question 38

A 5.0-kg crate is on an incline that makes an angle 30 $\degree$ with the horizontal. If the coefficient of static friction is 0.5, the maximum force that can be applied parallel to the plane without moving the crate is:

A) 0 N
B) 3.3 N
C) 21 N
D) 46 N
E) 55 N

Question 39

A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If $\mu$ _s = 0.60 and $\mu$ _k = 0.50, the acceleration of the block is:

A) 0 m/s²
B) 3.8 m/s²
C) 4.8 m/s²
D) 8.0 m/s²
E) 9.8 m/s²

Question 40

The system shown remains at rest. The force of friction on the block on the slope is:

A) 4 N
B) 8 N
C) 12 N
D) 16 N
E) 20 N

Question 41

The driver of a 1000-kg car tries to turn through a circle of radius 100 m on an unbanked curve at a speed of 10 m/s. The actual frictional force between the tires and a slippery road has a magnitude of 900 N. The car:

A) slides into the inside of the curve
B) makes the turn
C) slows down due to the frictional force
D) will make the turn only if it goes faster
E) slides off to the outside of the curve

Question 42

Why do raindrops fall with constant speed during the later stages of their descent?

A) The gravitational force is the same for all drops
B) Air resistance just balances the force of gravity
C) The drops all fall from the same height
D) The force of gravity is negligible for objects as small as raindrops
E) Gravity cannot increase the speed of a falling object to more than 9.8 m/s

Question 43

The magnitude of the force required to cause an 0.04-kg object to move at 0.6 m/s in a circle of radius 1.0 m is:

A) 2.4 * 10^-2 N
B) 1.4 * 10^-2 N
C) 1.4 $\pi$ * 10^-2 N
D) 2.4 $\pi$ ² * 10^-2 N
E) 3.13 N

Question 44

An object of mass m and another object of mass 2m are each forced to move along a circle of radius 1.0 m at a constant speed of 1.0 m/s. The magnitudes of their accelerations are:

A) equal
B) in the ratio of : 1
C) in the ratio of 2 : 1
D) in the ratio of 4 : 1
E) zero

Question 45

A ball of mass m is thrown downward from the edge of a cliff with an initial speed that is three times the terminal speed. Initially the drag force on it is

A) upward and greater than mg
B) upward and less than mg
C) downward and greater than mg
D) downward and less than mg
E) downward and equal to mg

Question 46

If a satellite moves above the Earth's atmosphere in a circular orbit with constant speed, then:

A) its acceleration and velocity are in the same direction
B) the net force on it is zero
C) its velocity is constant
D) it will fall back to Earth when its fuel is used up
E) its acceleration is toward the Earth

Question 47

A baseball has a terminal speed of 42 m/s in air (ρ = 1.2 kg/m³). What would be its terminal speed in water (ρ = 1.0 x 10³ kg/m³)?

A) 0.05 m/s
B) 1.5 m/s
C) 18 m/s
D) 42 m/s
E) 1200 m/s

Question 48

A cube has a drag coefficient of 0.8. What would be the terminal velocity of a sugar cube 1 cm on a side in air (ρ = 1.2 kg/m³)? Take the density of sugar to be 1.6 x 10³ kg/m³.

A) 1.4 m/s
B) 5 m/s
C) 18 m/s
D) 60 m/s
E) 320 m/s

Question 49

Block A, with a mass of 10 kg, rests on a 30 $\degree$ incline. The coefficient of kinetic friction is 0.20. The attached string is parallel to the incline and passes over a massless, frictionless pulley at the top. Block B, with a mass of 3.0 kg, is attached to the dangling end of the string. The acceleration of B is:

A) 0.20 m/s², up
B) 0.20 m/s², down
C) 2.8 m/s², up
D) 2.8 m/s², down
E) 0 m/s²

Question 50

A coin is placed on a horizontal phonograph turntable. Let N be the normal force exerted by the turntable on the coin, f be the frictional force exerted by the turntable on the coin, and f_{s, max} be the maximum force of the static friction. The speed of the turntable is increased in small steps. If the coin does not slide, then

A) N increases, f increases, and f_{s, max} stays the same
B) N increases, f increases, and f_{s, max} increases
C) f increases and both N and f_{s, max} stay the same
D) N, f, and f_{s, max} all stay the same
E) N, f, and f_{s, max} all increase

Question 51

Block A, with a mass of 10 kg, rests on a 30 $\degree$ incline. The coefficient of kinetic friction is 0.20. The attached string is parallel to the incline and passes over a massless, frictionless pulley at the top. Block B, with a mass of 8.0 kg, is attached to the dangling end of the string. The acceleration of B is:

A) 0.69 m/s², up
B) 0.69 m/s², down
C) 2.6 m/s², up
D) 2.6 m/s², down
E) 0 m/s²

Question 52

A ball is thrown upward into the air with a speed that is greater than terminal speed. On the way up it slows down and, after its speed equals the terminal speed but before it gets to the top of its trajectory:

A) its speed is constant
B) it continues to slow down
C) it speeds up
D) its motion becomes jerky
E) none of the above

Question 53

In uniform circular motion,

A) the acceleration is always constant in magnitude and direction.
B) the velocity is always constant in magnitude and direction.
C) both the acceleration and the velocity are continually changing direction.
D) the velocity is always changing direction but the acceleration is always in the same direction.
E) the net force is always constant in magnitude and direction.

Question 54

A car rounds a 75-m radius curve at a constant speed of 18 m/s. A ball is suspended by a string from the ceiling the car and moves with the car. The angle between the string and the vertical is:

A) 0°
B) 1.4°
C) 24°
D) 90°
E) cannot be found without knowing the mass of the ball

Question 55

A 1000-kg airplane moves in straight flight at constant speed. The force of air friction is 1800 N. The net force on the plane is:

A) 0 N
B) 11600 N
C) 1800 N
D) 9800 N
E) none of these

Question 56

Uniform circular motion is the direct consequence of:

A) Newton's third law
B) a force that is always tangent to the path
C) an acceleration tangent to the path
D) a force of constant magnitude that is always directed away from the same fixed point
E) a force of constant magnitude that is always directed toward the same fixed point

Question 57

An object moving in a circle at constant speed:

A) must have only one force acting on it
B) is not accelerating
C) is held to its path by centrifugal force
D) has an acceleration of constant magnitude
E) has an acceleration that is tangent to the circle

Question 58

A 0.2-kg stone is attached to a string and swung in a circle of radius 0.6 m on a horizontal and frictionless surface. If the stone makes 150 revolutions per minute, the tension force of the string on the stone is:

A) 0.03 N
B) 0.2 N
C) 0.75 N
D) 1.96 N
E) 30 N

Question 59

In uniform circular motion,

A) the acceleration always points away from the center of the circle.
B) the velocity always points towards the center of the circle.
C) the acceleration and the velocity are always parallel.
D) the acceleration and the velocity are always perpendicular.
E) there is no fixed relationship between the direction of the acceleration and the direction of the velocity.

Question 60

A ball is thrown upward into the air with a speed that is greater than terminal speed. It lands at the place where it was thrown. During its flight the force of air resistance is the greatest:

A) just after it is thrown
B) halfway up
C) at the top of its trajectory
D) halfway down
E) just before it lands

Question 61

One end of a 1.0-m long string is fixed; the other end is attached to a 2.0-kg stone. The stone swings in a vertical circle, passing the bottom point at 4.0 m/s. The tension force of the string at this point is about:

A) 0 N
B) 12 N
C) 20 N
D) 32 N
E) 52 N

Question 62

An object moves around a circle. If the radius is doubled keeping the speed the same then the magnitude of the centripetal force must be:

A) twice as great
B) half as great
C) four times as great
D) one-fourth as great
E) the same

Question 63

One end of a 1.0-m string is fixed; the other end is attached to a 2.0-kg stone. The stone swings in a vertical circle, passing the top point at 4.0 m/s. The tension force of the string at this point is about:

A) 0 N
B) 12 N
C) 20 N
D) 32 N
E) 52 N

Question 64

An object moves in a circle. If the mass is tripled, the speed halved and the radius unchanged then the magnitude of the centripetal force must be multiplied by a factor of:

A) 3/2
B) 3/4
C) 9/4
D) 6
E) 12

Question 65

An 800-N passenger in a car presses against the car door with a 200 N force when the car makes a left turn at 13 m/s. The (faulty) door will pop open under a force of 800 N. Of the following, the least speed for which the man is thrown out of the car is:

A) 14 m/s
B) 19 m/s
C) 20 m/s
D) 26 m/s
E) 52 m/s

Question 66

A giant wheel, having a diameter of 40 m, is fitted with a cage and platform on which a man of mass m stands. The wheel is rotated in a vertical plane at such a speed that the force exerted by the man on the platform is equal to his weight when the cage is at X, as shown. The net force on the man at point X is:

A) 0
B) mg, down
C) mg, up
D) 2 mg, down
E) 2 mg, up

Question 67

The iron ball shown is being swung in a vertical circle at the end of a 0.7-m string. How slowly can the ball go through its top position without having the string go slack?

A) 1.3 m/s
B) 2.6 m/s
C) 3.9 m/s
D) 6.9 m/s
E) 9.8 m/s

Question 68

A person riding a Ferris wheel is strapped into her seat by a seat belt. The wheel is spun so that the centripetal acceleration is g. Select the correct combination of forces that act on her when she is at the top. Here, F_g = force of gravity, down; F_b = seat belt force, down; and F_s = seat force, up.

A) F_g = 0, F_b = mg, F_s = 0
B) F_g = mg, F_b = 0, F_s = 0
C) F_g = 0, F_b = 0, F_s = mg
D) F_g = mg, F_b = mg, F_s = 0
E) F_g = mg, F_b = 0, F_s = mg

Question 69

Circular freeway entrance and exit ramps are commonly banked to handle a car moving at 13 m/s. To design a similar ramp for 26 m/s one should:

A) increase the radius by a factor of 2
B) decrease the radius by a factor of 2
C) increase the radius by a factor of 4
D) decrease the radius by a factor of 4
E) increase the radius by a factor of

Question 70

If a certain car, going with speed v₁, rounds a level curve with a radius R₁, it is just on the verge of skidding. If its speed is now doubled, the radius of the tightest curve on the same road that it can round without skidding is:

A) 2R₁
B) 4R₁
C) R₁/2
D) R₁/4
E) R₁

Question 71

An automobile moves on a level horizontal road in a circle of radius 30 m. The coefficient of friction between tires and road is 0.50. The maximum speed with which this car can round this curve is:

A) 3.0 m/s
B) 4.9 m/s
C) 9.8 m/s
D) 12 m/s
E) 147 m/s

Question 72

Which of the following five graphs is correct for a particle moving in a circle of radius r at a constant speed of 10 m/s?

A) I
B) II
C) III
D) IV
E) V

Question 73

A giant wheel, 40 m in diameter, is fitted with a cage and platform on which a man can stand. The wheel rotates at such a speed that when the cage is at X (as shown) the force exerted by the man on the platform is equal to his weight. The speed of the man is:

A) 14 m/s
B) 20 m/s
C) 28 m/s
D) 80 m/s
E) 120 m/s

Question 74

At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12 m/s even if the roadway is icy (and the frictional force is zero)?

A) 0°
B) 16°
C) 17°
D) 35°
E) 73°