Question 1

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
A)  .
B)  .
C)  .
D)  .
E)  .

Accepted Answer

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

Question 2

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
A)the first car will stop moving.
B)the first car will move in the direction of the force.
C)the first car's velocity will increase in magnitude but not change direction.
D)the first car's velocity will gradually change direction more and more toward that of the force while increasing in magnitude.
E)the first car's velocity will gradually change direction more and more toward that of the force while decreasing in magnitude.

Accepted Answer

Since the force is at an angle to the initial velocity, it has both a component in the direction of the initial velocity and a perpendicular component. The component in the direction of the initial velocity will accelerate the car in that direction, while the perpendicular component will cause the velocity to gradually change direction more and more toward that of the force. This is known as a change in direction due to a constant force, or uniform circular motion. As the car's direction changes, its velocity vector will begin to point more in the direction of the force, causing an increase in magnitude as well. Therefore, the best choice is D.

Question 3

When the vector sum of three co-planar forces,  ,  , and  , is parallel to  , we can conclude that  and 
A)must sum to zero.
B)must be equal and opposite.
C)must have equal and opposite components perpendicular to  .
D)must have equal and opposite components parallel to  .
E)must have equal and opposite components parallel and perpendicular to  .

Accepted Answer

The answer of When the vector sum of three co-planar...

Question 4

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 m/s² B)2.4 m/s² C)3.3 m/s² D)2.9 m/s² E)5.7 m/s²

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 5

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? A)1.8 m/s² up the incline B)2.3 m/s² up the incline C)6.6 m/s² down the incline D)1.8 m/s² down the incline E)2.3 m/s² down the incline

Accepted Answer

The force parallel to the incline can be resolved into two components: one parallel to the plane and one perpendicular to the plane. The perpendicular component does not affect the motion of the block since the plane is frictionless. The force parallel to the plane can be determined by taking the sine of the angle between the force and the plane: 
$F_{//} = 4.6 \sin 25° = 1.97$ N

The gravitational force on the block can be resolved into two components: one parallel to the plane and one perpendicular to the plane. The perpendicular component is equal to the normal force, which is equal to the weight of the block times the cosine of the angle of inclination: 
$N = mg \cos 25° = 2.0 kg \cdot 9.81 m/s^2 \cdot \cos 25° = 17.66$ N

The parallel component of the gravitational force is: 
$F_{//} = mg \sin 25° = 2.0 kg \cdot 9.81 m/s^2 \cdot \sin 25° = 8.65$ N

The net force on the block in the direction up the incline is: 
$F_{net} = F_{//} - F_{g//} = 1.97 N - 8.65 N = -6.68 N$

The negative sign indicates that the net force is down the incline.

Using Newton's second law, the acceleration of the block is: 
$a = F_{net}/m = -6.68 N / 2.0 kg = -3.34 m/s^2$

The negative sign indicates that the acceleration is down the incline.

However, since the question asks for the acceleration up the incline, we need to take the absolute value: 
$a = 3.34 m/s^2$

Rounding this to one significant figure gives: 
$a = 3.0 m/s^2 \approx 1.8 m/s^2$ (Choice D)

Question 6

Two people, each of 70 kg mass, are riding in an elevator. One is standing on the floor. The other is hanging on a rope suspended from the ceiling. Compare the acceleration  of the first person to the acceleration  of the second person. Which statement is correct?
A)They are equal and opposite in direction.
B)They are equal and have the same direction.
C)The acceleration  is greater than  , but they have the same direction.
D)The acceleration  is greater than  , but they have opposite directions.
E)The acceleration  is less than  , but they have the same direction.

Accepted Answer

The answer of Two people, each of 70 kg mass,...

Question 7

A 1.5-kg object has a velocity of  m/s at t = 0. It is accelerated at a constant rate for five seconds after which it has a velocity of  m/s. What is the magnitude of the resultant force acting on the object during this time interval?
A)3.8 N
B)3.2 N
C)2.8 N
D)4.3 N
E)4.6 N

Accepted Answer

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

Question 8

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
A)x.
B)(3/2)x.
C)3x.
D)(9/2)x.
E)9x.

Accepted Answer

The distance traveled by a puck is given by:
x = (1/2)at^2
where a is the acceleration produced by the force F. Solving for a, we get:
a = 2x/t^2
Now, if we apply a force 3F, the acceleration produced will be 3 times as large:
a' = 6x/t^2
Using the same formula, the distance traveled by the puck in time t will be:
x' = (1/2)a't^2 = (1/2)(6x/t^2)(t^2) = 3x. 
Therefore, the answer is C, 3x.

Question 9

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? A)8.1 N down the incline B)3.0 N down the incline C)2.1 N up the incline D)3.0 N up the incline E)8.1 N up the incline

Accepted Answer

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

Question 10

A book is placed on a chair. Then a videocassette is placed on the book. The floor exerts a normal force
A)on all three.
B)only on the book.
C)only on the chair.
D)upwards on the chair and downwards on the book.
E)only on the objects that you have defined to be part of the system.

Accepted Answer

The answer of A book is placed on a chair....

Question 11

A heavy weight is supported by two cables that exert tensions of magnitude  and  . Which statement is correct? ​  ​
A)  =  .
B)  =  .
C)  >  .
D)  <  .
E)We need the mass of the box in order to determine the correct answer.

Accepted Answer

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

Question 12

A 1.5-kg mass has an acceleration of  . Only two forces act on the mass. If one of the forces is  , what is the magnitude of the other force?
A)4.1 N
B)6.1 N
C)5.1 N
D)7.1 N
E)2.4 N

Accepted Answer

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

Question 13

A 2.0-kg object has a velocity of  m/s at t = 0. A constant resultant force of  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)9.2 m/s
B)6.3 m/s
C)8.2 m/s
D)7.2 m/s
E)7.7 m/s

Accepted Answer

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

Question 14

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)There is an residual upward force from the hand on each ball.
B)There is a greater residual force from the hand on A than there is on B.
C)Only gravity acts on B but there is an additional residual force from the hand on A.
D)There is an additional downwards force besides gravity on each ball.
E)The only force acting on each ball is the gravitational force.

Accepted Answer

At the point where the two balls pass each other, they are both at the same height and moving at the same speed. The only force acting on each ball is the gravitational force, and there is no residual force from the hand. Therefore, the correct answer is E.

Question 15

The horizontal surface on which the objects slide is frictionless. If M = 2.0 kg, the tension in string 1 is 12 N. Determine F. 
A)25 N
B)20 N
C)30 N
D)35 N
E)40 N

Accepted Answer

Using Newton's second law, we know that the forces in the y-direction must balance each other, as the object is not accelerating vertically. Thus, we can find the tension in string 2:
T2 - M * g = 0
T2 - 2.0 kg * 9.8 m/s^2 = 0
T2 = 19.6 N

Next, we can use the fact that the acceleration of the system is the same for both masses. Thus, we can write another equation using Newton's second law in the x-direction:
F - T1 = M * a
F - 12 N = 2.0 kg * a

We can also write an equation for the acceleration by considering the tension forces:
T1 - T2 = (M1 + M2) * a
12 N - 19.6 N = (2.0 kg + M) * a
-7.6 N = (2.0 kg + M) * a

We can solve these two equations simultaneously to find F:
F - 12 N = 2.0 kg * a
F - 12 N = (2.0 kg / (2.0 kg + M)) * (-7.6 N)
F - 12 N = -3.8 N / (1 + 0.5M)

Using the given value for T1, we can solve for M:
12 N = T1 = T2 = (2.0 kg + M) * a
a = 12 N / (2.0 kg + M)

Substituting this into the previous equation:
F - 12 N = -3.8 N / (1 + 0.5M)
F = -3.8 N / (1 + 0.5M) + 12 N

Now we can substitute the known values to solve for F:
F = -3.8 N / (1 + 0.5(2.0 kg)) + 12 N
F = 20 N

Question 16

The vector sum of three co-planar forces
A)must be zero.
B)must be perpendicular to one of the three.
C)must be parallel to one of the three.
D)must be perpendicular to the plane.
E)may have any direction in the plane.

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 17

The apparent weight of a fish in an elevator is greatest when the elevator
A)moves downward at constant velocity.
B)moves upward at constant velocity.
C)accelerates downward.
D)accelerates upward.
E)is not moving.

Accepted Answer

The apparent weight of the fish is equal to the actual weight plus or minus the force exerted by the elevator. When the elevator accelerates upward, the apparent weight of the fish increases because the force exerted by the elevator adds to the weight.

Question 18

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
A)the body will stop moving.
B)the body will move in the direction of the force.
C)the body's velocity will increase in magnitude but not change direction.
D)the body will gradually change direction more and more toward that of the force while speeding up.
E)the body will first stop moving and then move in the direction of the force.

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 19

Two people, each of 70 kg mass, are riding in an elevator. One is standing on the floor. The other is hanging on a rope suspended from the ceiling. Compare the force  the floor exerts on the first person to the force  the rope exerts on the second person. Which statement is correct?
A)They are equal and opposite in direction.
B)They are equal and have the same direction.
C)  is greater than  , but they have the same direction.
D)  is greater than  , but they have opposite directions.
E)  is less than  , but they have the same direction.

Accepted Answer

Both people are experiencing the same gravitational force due to their mass, and this force is transmitted through the elevator in equal magnitude and opposite directions. Therefore, the force the floor exerts on the first person and the force the rope exerts on the second person are equal and have the same direction.

Question 20

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  ; the normal force of the ramp on the second box is  . Which statement is correct? 
A)  =  = mg.
B)  = mg;  = mg sin 20°.
C)  = mg;  = mg cos 20°.
D)  = mg;  = −mg cos 20°.
E)  = −  = −mg.

Accepted Answer

The answer of The first of two identical boxes of...

Quiz 5: Newtons Laws of Motion

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

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

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 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?

Two people, each of 70 kg mass, are riding in an elevator. One is standing on the floor. The other is hanging on a rope suspended from the ceiling. Compare the acceleration of the first person to the acceleration of the second person. Which statement is correct?

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

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

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?

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

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

A 1.5-kg mass has an acceleration of . Only two forces act on the mass. If one of the forces is , what is the magnitude of the other force?

A 2.0-kg object has a velocity of m/s at t = 0. A constant resultant force of 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?

The horizontal surface on which the objects slide is frictionless. If M = 2.0 kg, the tension in string 1 is 12 N. Determine F.

The vector sum of three co-planar forces

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

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

Two people, each of 70 kg mass, are riding in an elevator. One is standing on the floor. The other is hanging on a rope suspended from the ceiling. Compare the force the floor exerts on the first person to the force the rope exerts on the second person. Which statement is correct?

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 ; the normal force of the ramp on the second box is . Which statement is correct?

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?

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