Question 1

A constant force is applied to a body that is already moving. The force is directed at an angle of 60 degrees to the direction of the body's velocity. What is most likely to happen is that

Accepted Answer

When a constant force is applied at an angle to the direction of motion, it has two components: one along the direction of motion that changes the speed, and one perpendicular to it that changes the direction. Over time, this causes the body to gradually change its direction towards the force while its speed increases.

Question 2

Only two forces act on a 3.0-kg mass. One of the forces is 9.0 N east, and the other is 8.0 N in the direction of 62° north of west. What is the magnitude of the acceleration of the mass?

Accepted Answer

To find the magnitude of the acceleration, we first need to find the resultant force acting on the mass. The forces can be broken down into their components:- The 9.0 N force is entirely in the east direction (x-axis).- The 8.0 N force at 62° north of west can be broken down into x and y components:  - $F_x = 8.0 \cos(62°)$ (west direction, so it will be negative when combined with the eastward force)  - $F_y = 8.0 \sin(62°)$ (north direction)Calculating these components:- $F_x = -8.0 \cos(62°) \approx -3.8$ N (west)- $F_y = 8.0 \sin(62°) \approx 7.1$ N (north)The net force in the x-direction (east-west) is:- $F_{net,x} = 9.0 - 3.8 = 5.2$ N (east)Since there's no other force in the y-direction in the problem statement, the net force in the y-direction is just $F_y = 7.1$ N (north).The magnitude of the net force is found using Pythagoras' theorem:- $F_{net} = \sqrt{F_{net,x}^2 + F_{y}^2} = \sqrt{5.2^2 + 7.1^2} \approx 8.7$ NFinally, using Newton's second law ($F = ma$), the magnitude of the acceleration ($a$) can be found by dividing the net force by the mass:- $a = \frac{F_{net}}{m} = \frac{8.7}{3.0} \approx 2.9$ m/s$^2$Therefore, the correct answer is D) 2.9 m/s$^2$.

Question 3

A 2.0-kg object has a velocity of 4.0  m/s at t = 0. A constant resultant force of (2.0  + 4.0  ) N then acts on the object for 3.0 s. What is the magnitude of the object's velocity at the end of the 3.0-s interval?

Accepted Answer

The answer of A 2.0-kg object has a velocity of...

Question 4

A juggler throws two balls up to the same height so that they pass each other halfway up when A is rising and B is descending. Ignore air resistance and buoyant forces. Which statement is true of the two balls at that point?

Accepted Answer

At the point where the balls pass each other halfway up, the only force acting on each ball is the gravitational force. There is no residual force from the hand, as the balls have been released and are in free fall. Additionally, there is no additional downwards force on each ball.

Question 5

A 1.5-kg mass has an acceleration of (4.0 − 3.0 ) m/s². Only two forces act on the mass. If one of the forces is (2.0 − 1.4 ) N, what is the magnitude of the other force?

Accepted Answer

The answer of A 1.5-kg mass has an acceleration of...

Question 6

A 1.5-kg object has a velocity of 5  m/s at t = 0. It is accelerated at a constant rate for five seconds after which it has a velocity of (6  + 12  ) m/s. What is the direction of the resultant force acting on the object during this time interval?

Accepted Answer

The answer of A 1.5-kg object has a velocity of...

Question 7

A 2.0-kg block slides on a frictionless 15° inclined plane. A force acting parallel to the incline is applied to the block. The acceleration of the block is 1.5 m/s² down the incline. What is the applied force?

Accepted Answer

The answer of A 2.0-kg block slides on a frictionless...

Question 8

The total force needed to drag a box at constant speed across a surface with coefficient of kinetic friction μ_k is least when the force is applied at an angle θ such that

Accepted Answer

The minimum force needed to drag a box at constant speed is when the force is applied at an angle θ such that the component of force parallel to the surface is equal and opposite to the force of friction. This can be represented by the equation Fcosθ = μkFn, where F is the total force, θ is the angle between the force and the surface, μk is the coefficient of kinetic friction, and Fn is the normal force. Solving for cosθ, we get cosθ = μk. Therefore, the best choice is C, tanθ = μk.

Question 9

When the vector sum of three co-planar forces,  ,  and  , is parallel to  , we can conclude that  and

Accepted Answer

If the vector sum of three co-planar forces is parallel to a vector, it means that the forces have a common component in the direction of that vector. Therefore, the component of forces 11eb6adc_ed60_1afa_b0cf_c79a3cf7c03a_TB8245_11 and 11eb6adc_ed60_420b_b0cf_0bc35dfdea1a_TB8245_11 perpendicular to 11eb6adc_ed60_691c_b0cf_b7f1fbdea7d9_TB8245_11 must cancel out the common component of the three forces parallel to 11eb6adc_ed60_1af9_b0cf_53b501c1e03b_TB8245_11. This means that both forces must have equal and opposite components perpendicular to 11eb6adc_ed60_691c_b0cf_b7f1fbdea7d9_TB8245_11 (Choice C). It is not necessary for the forces to have equal and opposite components parallel to 11eb6adc_ed60_691d_b0cf_03308a03f7b4_TB8245_11 or equal and opposite components parallel and perpendicular to 11eb6adc_ed60_902e_b0cf_733e80e793b1_TB8245_11, so Choices D and E are incorrect. Choice A is incorrect because the forces do not have to sum to zero in order to have a vector sum parallel to another vector. Choice B is incorrect because the forces do not have to be equal in magnitude in order to have a vector sum parallel to another vector.

Question 10

The first of two identical boxes of mass m is sitting on level ground. The second box is sitting on a ramp that makes a 20° angle with the ground. The normal force of the level ground on the first box is N_L; the normal force of the ramp on the second box is N_R. Which statement is correct?

Accepted Answer

For the box on level ground, the normal force equals the gravitational force acting on it, which is mg. For the box on the ramp, the normal force is the component of the gravitational force perpendicular to the surface of the ramp, which is mg cos(20°).

Question 11

The vector sum of three co-planar forces

Accepted Answer

The vector sum of three co-planar forces can result in a vector of any direction within the plane, depending on the magnitudes and directions of the individual forces.

Question 12

A constant force F is applied to a body of mass m that initially is headed east at velocity v₀ until its velocity becomes −v₀. The total time of travel is 2t. The total distance the body travels in that time is

Accepted Answer

The answer of A constant force F is applied to...

Question 13

A 1.5-kg object has a velocity of 5  m/s at t = 0. It is accelerated at a constant rate for five seconds after which it has a velocity of (6  + 12  ) m/s. What is the magnitude of the resultant force acting on the object during this time interval?

Accepted Answer

The answer of A 1.5-kg object has a velocity of...

Question 14

A book is placed on a chair. Then a videocassette is placed on the book. The floor exerts a normal force

Accepted Answer

The floor exerts a normal force upwards on the chair, which in turn supports the book and videocassette. The normal force from the floor does not act directly on the book or videocassette.

Question 15

The first of two identical boxes of mass m is sitting on level ground. The second box is sitting on a ramp that makes an angle with the ground. When a force of magnitude F is applied to each box in a direction parallel to the surface it is on, upwards on the box on the ramp, neither box moves. Which statement comparing the friction force on the box on the level, f_L, to the friction force on the box on the ramp, f_R, is correct?

Accepted Answer

The friction force depends on the normal force, which is different for the box on the ramp due to the angle. Without specific values for the angle, mass, applied force, and coefficient of static friction, any of the scenarios (a, b, or c) could be correct.

Question 16

The apparent weight of a fish in an elevator is greatest when the elevator

Accepted Answer

The apparent weight of the fish is equal to the normal force acting on it by the elevator floor. When the elevator accelerates upward, the normal force acting on the fish (and thus the apparent weight) increases. Similarly, when the elevator accelerates downward, the normal force (and apparent weight) decreases. When the elevator is moving at constant velocity or is not moving, the normal force and apparent weight of the fish are the same as its actual weight. Therefore, the greatest apparent weight of the fish occurs when the elevator accelerates upward.

Question 17

You have a machine which can accelerate pucks on frictionless ice. Starting from rest, the puck travels a distance x in time t when force F is applied. If force 3F is applied, the distance the puck travels in time t is

Accepted Answer

The distance traveled by the puck is directly proportional to the force applied and the time taken. So, if the force is tripled, the distance covered will also be tripled. Therefore, the distance the puck travels in time t when a force 3F is applied is 3x.

Question 18

A heavy weight is supported by two cables that exert tensions of magnitude T₁ and T₂. Which statement is correct?

Accepted Answer

The answer of A heavy weight is supported by two...

Question 19

A bumper car is moving at constant velocity when another bumper car starts to push on it with a constant force at an angle of 60 degrees with respect to the first car's initial velocity. The second bumper car continues pushing in exactly that direction for some time. What is most likely to happen is that

Accepted Answer

Since the force is at an angle of 60 degrees with the initial velocity, it has components in both the horizontal and vertical directions. The vertical component is perpendicular to the direction of motion and does not affect the motion of the first car. The horizontal component is in the direction of the force and will cause the first car's velocity to gradually change direction more and more toward that of the force while increasing in magnitude. This is consistent with the idea of an unbalanced force causing an acceleration, which changes the velocity of the first car.

Question 20

A 2.0-kg block slides on a frictionless 25° inclined plane. A force of 4.6 N acting parallel to the incline and up the incline is applied to the block. What is the acceleration of the block?

Accepted Answer

First, we need to find the component of the force parallel to the incline. This would be Fpar = Fsin(25°) = 4.6 sin(25°) = 1.98 N.
Next, we can use Newton's second law in the direction parallel to the incline:
Fpar = ma
1.98 N = 2.0 kg * a
a = 0.99 m/s^2.
Since the force is up the incline and the acceleration is down the incline, the answer is 1.8 m/s^2 down the incline (which is the negative of 0.99 m/s^2).

Quiz 5: The Laws of Motion

A constant force is applied to a body that is already moving. The force is directed at an angle of 60 degrees to the direction of the body's velocity. What is most likely to happen is that

Only two forces act on a 3.0-kg mass. One of the forces is 9.0 N east, and the other is 8.0 N in the direction of 62° north of west. What is the magnitude of the acceleration of the mass?

A 2.0-kg object has a velocity of 4.0 m/s at t = 0. A constant resultant force of (2.0 + 4.0 ) N then acts on the object for 3.0 s. What is the magnitude of the object's velocity at the end of the 3.0-s interval?

A juggler throws two balls up to the same height so that they pass each other halfway up when A is rising and B is descending. Ignore air resistance and buoyant forces. Which statement is true of the two balls at that point?

A 1.5-kg mass has an acceleration of (4.0 − 3.0 ) m/s2. Only two forces act on the mass. If one of the forces is (2.0 − 1.4 ) N, what is the magnitude of the other force?

A 1.5-kg object has a velocity of 5 m/s at t = 0. It is accelerated at a constant rate for five seconds after which it has a velocity of (6 + 12 ) m/s. What is the direction of the resultant force acting on the object during this time interval?

A 2.0-kg block slides on a frictionless 15° inclined plane. A force acting parallel to the incline is applied to the block. The acceleration of the block is 1.5 m/s2 down the incline. What is the applied force?

The total force needed to drag a box at constant speed across a surface with coefficient of kinetic friction μk is least when the force is applied at an angle θ such that

When the vector sum of three co-planar forces, , and , is parallel to , we can conclude that and

The first of two identical boxes of mass m is sitting on level ground. The second box is sitting on a ramp that makes a 20° angle with the ground. The normal force of the level ground on the first box is NL; the normal force of the ramp on the second box is NR. Which statement is correct?