Question 1

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

Accepted Answer

The answer of Block A, with a mass of 10...

Question 2

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

Accepted Answer

Since the horizontal force is used to push the book against the wall, it does not contribute to the book's acceleration in the horizontal direction. The only forces acting on the book in the vertical direction are its weight and the normal force from the wall, which balance each other out. Therefore, there is no net force to cause acceleration, meaning the book remains at rest or moves at a constant velocity if it was already in motion. The coefficients of static and kinetic friction provided are not relevant to the calculation of acceleration in this context.

Question 3

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

Accepted Answer

The answer of A block is first placed on its...

Question 4

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

Accepted Answer

The answer of A 50-N force is applied to a...

Question 5

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

Accepted Answer

The answer of A box rests on a rough board...

Question 6

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

Accepted Answer

When the block slides down at a constant speed, it means that the force of friction is equal and opposite to the component of gravitational force parallel to the plane. In this case:
$$F_{friction} = F_{gravity}\sin 30^\circ$$
$$\mu_k F_{normal} = mg\sin 30^\circ$$
where $\mu_k$ is the coefficient of kinetic friction, $F_{normal}$ is the normal force exerted on the block by the plane, and $m$ is the mass of the block. The normal force is equal and opposite to the component of gravitational force perpendicular to the plane:
$$F_{normal} = mg\cos 30^\circ$$
Putting it all together, we get:
$$\mu_k = \frac{mg\sin 30^\circ}{mg\cos 30^\circ} = 	an 30^\circ = \boxed{0.577}$$

Question 7

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

Accepted Answer

The answer of Block A, with mass m_A, is initially...

Question 8

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

Accepted Answer

The answer of Block A, with a mass of 50...

Question 9

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.

Accepted Answer

The answer of The same heavy wooden block is dragged...

Question 10

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

Accepted Answer

The answer of A 5.0-kg crate is on an incline...

Question 11

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

Accepted Answer

The answer of A crate resting on a rough horizontal...

Question 12

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

Accepted Answer

The answer of A 5.0-kg crate is resting on a...

Question 13

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

Accepted Answer

The answer of A horizontal force of 12 N pushes...

Question 14

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

Accepted Answer

The answer of A crate is sliding down an incline...

Question 15

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

Accepted Answer

The answer of A horizontal force of 5.0 N pushes...

Question 16

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

Accepted Answer

The answer of Block A, with a mass of 10...

Question 17

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

Accepted Answer

First, we need to find the normal force acting on the crate. To do this, we need to resolve the weight force into its components perpendicular and parallel to the plank.

The perpendicular force is given by: 
N = mg cosθ 
where m is the mass of the crate, g is the acceleration due to gravity, and θ is the angle of the plank with respect to the horizontal. 
N = (5.0 kg)(9.81 m/s^2) cos(25°) = 45.3 N

The parallel force is given by: 
F = mg sinθ 
F = (5.0 kg)(9.81 m/s^2) sin(25°) = 21 N

We can now determine whether the crate remains at rest or moves down the plank.

The maximum force of static friction is: 
f_smax = μ_s N 
where μ_s is the coefficient of static friction. 
f_smax = (0.50)(45.3 N) = 22.6 N

Since the parallel force is less than the maximum force of static friction, the crate remains at rest. Therefore, the force of friction acting on the crate is maximum force of static friction, or 22.6 N.

However, the question asks for the force of friction after the end of the plank is raised, implying that the crate is now moving down the plank. In this case, the force of kinetic friction comes into play.

The force of kinetic friction is given by: 
f_k = μ_k N 
where μ_k is the coefficient of kinetic friction. 
f_k = (0.40)(45.3 N) = 18.1 N

Therefore, the force of friction acting on the crate after the end of the plank is raised is 18.1 N, which is closest to choice C (21 N).

Question 18

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

Accepted Answer

The maximum force that can be applied parallel to the plane without moving the crate is given by the equation Fmax = μsN, where μs is the coefficient of static friction and N is the normal force. The normal force is equal to the component of the weight of the crate that is perpendicular to the plane, which is given by N = mgcos(θ), where θ is the angle of the incline and g is the acceleration due to gravity.

Substituting the given values, we get N = (5.0 kg)(9.81 m/s^2)cos(30°) = 42.7 N.

Then, using the coefficient of static friction μs = 0.5, we can find the maximum force that can be applied without moving the crate:

Fmax = μsN = (0.5)(42.7 N) = 21.4 N.

Therefore, the closest choice is D) 46 N, which is the next-highest choice after 21.4 N.

Question 19

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

Accepted Answer

The answer of A horizontal force of 5.0 N pushes...

Question 20

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

Accepted Answer

Since the system is at rest, the net force on the block must be zero. The only forces acting on the block are its weight (mg) and the frictional force (Ff). Therefore, Ff = mg sin(30°) = (5 kg)(9.8 m/s²)(sin 30°) = 24.5 N. The frictional force of 24.5 N opposes the tendency of the block to slide down the slope, and the force of gravity is resolved into two components: one component is parallel to the slope and is balanced by the frictional force, while the other component is perpendicular to the slope and is balanced by the normal force of the slope on the block. The only answer choice that is close to Ff = 24.5 N is B = 8 N.

Quiz 6: Force and Motion II

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 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 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 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 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 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 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 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 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 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 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 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 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 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:

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

Quiz 6: Force and Motion II

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 mB, attached to the dangling end, for which A remains at rest is:

A horizontal force of 12 N pushes a 0.50-kg book against a vertical wall. The book is initially at rest. If μ\muμ s = 0.60 and μ\muμ k = 0.50, the acceleration of the book is:

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 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 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 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 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 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 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 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 μ\muμ s = 0.60 and μ\muμ k = 0.50 which of the following is true?

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 horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If μ\muμ s = 0.60 and μ\muμ k = 0.50, the frictional force after a period of time is:

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 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 horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If μ\muμ s = 0.60 and μ\muμ k = 0.50, the acceleration of the block is: