Question 1

A 2.0 kg mass is moving along the x-axis. The potential energy curve as a function of position is shown in the figure. The kinetic energy of the object at the origin is 12 J. The system is conservative,and there is no friction.  
(a) What will be the kinetic energy at 2.0 m along the +x-axis?
(b) What will be the speed of the object at 6.0 m along the +x-axis?

Accepted Answer

The answer of A 2.0 kg mass is moving along...

Question 2

You swing a bat and hit a heavy box with a force of 1500 N.The force the box exerts on the bat is
A) exactly 1500 N only if the box does not move.
B) exactly 1500 N whether or not the box moves.
C) greater than 1500 N if the box moves.
D) less than 1500 N if the box moves.
E) greater than 1500 N if the bat bounces back.

Accepted Answer

According to Newton's Third Law of Motion, every action has an equal and opposite reaction. In this case, the action is the force with which the bat hits the box (1500 N) and the reaction is the force with which the box hits the bat. Therefore, the force the box exerts on the bat is also 1500 N, regardless of whether or not the box moves.

Question 3

A stalled car is being pushed up a hill at constant velocity by three people.The net force on the car is
A) zero.
B) up the hill and equal to the weight of the car.
C) down the hill and equal to the weight of the car.
D) up the hill and greater than the weight of the car.
E) down the hill and greater than the weight of the car.

Accepted Answer

Since the car is being pushed up the hill at a constant velocity, it means that the net force on the car is zero. This is because the force provided by the three people pushing the car up the hill is equal and opposite to the force of friction acting against the car rolling on the hill. Therefore, the net force on the car is zero.

Question 4

Consider what happens when you jump up in the air.Which of the following is the most accurate statement? A) It is the upward force exerted by the ground that pushes you up, but this force cannot exceed your weight. B) You are able to spring up because the earth exerts a force upward on you that is greater than the downward force you exert on the earth. C) Since the ground is stationary, it cannot exert the upward force necessary to propel you into the air. Instead, it is the internal forces of your muscles acting on your body itself that propels your body into the air. D) When you push down on the earth with a force greater than your weight, the earth will push back with the same magnitude force and thus propel you into the air. E) When you jump up the earth exerts a force F₁ on you and you exert a force F₂ on the earth. You go up because F₁ > F₂.

Accepted Answer

The answer of Consider what happens when you jump up...

Question 5

In order to lift a bucket of concrete,you must pull up harder on the bucket than it pulls down on you.

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, the force you exert to lift the bucket is equal in magnitude and opposite in direction to the gravitational force the bucket exerts downward.

Question 6

Two weights are connected by a massless wire and pulled upward with a constant speed of 1.50 m/s by a vertical pull P.The tension in the wire is T (see figure).Which one of the following relationships between T and P must be true? 
A) T > P
B) T = P
C) P + T = 125 N
D) P = T + 25 N
E) P = T + 100 N

Accepted Answer

Since the weights are moving with a constant speed, the net force on them is zero. Therefore, the upward force from the tension in the wire must be equal and opposite to the downward force of gravity on the weights. The weight of each object is given by:

w = mg

where m is the mass of the object and g is the acceleration due to gravity (9.81 m/s²). Since the objects have equal masses, their weights are equal:

w = m1g + m2g = 5 kg × 9.81 m/s² = 49.05 N

The tension in the wire is given by:

T = P - w

Therefore,

P = T + w

We can see that choice D is the only one that matches this relationship. Therefore, the correct answer is D.

Question 7

A 615 N student standing on a scale in an elevator notices that the scale reads 645 N.From this information,the student knows that the elevator must be moving
A) downward.
B) upward.
C) You cannot tell if it is moving upward or downward.

Accepted Answer

The answer of A 615 N student standing on a...

Question 8

A 20-ton truck collides with a 1500-lb car and causes a lot of damage to the car.During the collision
A) the force on the truck due to the collision is slightly greater than the force on the car.
B) the force of on the truck due to the collision is exactly equal to the force on the car.
C) the force on the car due to the collision is much greater than the force on the truck.
D) the car and the truck have the same magnitude acceleration.

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that the force exerted by the truck on the car is exactly equal in magnitude to the force exerted by the car on the truck during the collision.

Question 9

Which one of the following free-body diagrams best represents the free-body diagram,with correct relative force magnitudes,of a person in an elevator that is traveling upward but is gradually slowing down at a rate of 9 m/s²? _f is the force of the floor on the person and _g is the force of gravity on the person. A) B) C) D) E)

Accepted Answer

The answer of Which one of the following free-body diagrams...

Question 10

A 2.00-kg object traveling east at 20.0 m/s collides with a 3.00-kg object traveling west at 10.0 m/s. After the collision,the 2.00-kg object has a velocity 5.00 m/s to the west. How much kinetic energy was lost during the collision?
A) 0.000 J
B) 458 J
C) 516 J
D) 91.7 J
E) 175 J

Accepted Answer

The kinetic energy before the collision can be calculated using the formula $KE = \frac{1}{2}mv^2$ for each object and then summing them up. For the 2.00-kg object, $KE_1 = \frac{1}{2}(2.00\, \text{kg})(20.0\, \text{m/s})^2 = 400\, \text{J}$. For the 3.00-kg object, $KE_2 = \frac{1}{2}(3.00\, \text{kg})(10.0\, \text{m/s})^2 = 150\, \text{J}$. The total initial kinetic energy is $400\, \text{J} + 150\, \text{J} = 550\, \text{J}$.After the collision, the 2.00-kg object has a velocity of 5.00 m/s to the west. The kinetic energy of this object is $KE_{1, \text{after}} = \frac{1}{2}(2.00\, \text{kg})(5.00\, \text{m/s})^2 = 25\, \text{J}$. To find the velocity of the 3.00-kg object after the collision, we use the conservation of momentum, since momentum is conserved in collisions. The initial momentum is $p_{\text{initial}} = (2.00\, \text{kg})(20.0\, \text{m/s}) + (3.00\, \text{kg})(-10.0\, \text{m/s}) = 40\, \text{kg}\cdot\text{m/s} - 30\, \text{kg}\cdot\text{m/s} = 10\, \text{kg}\cdot\text{m/s}$.After the collision, the momentum of the 2.00-kg object is $(2.00\, \text{kg})(-5.00\, \text{m/s}) = -10\, \text{kg}\cdot\text{m/s}$. To conserve momentum, the 3.00-kg object must have a momentum of $10\, \text{kg}\cdot\text{m/s} + 10\, \text{kg}\cdot\text{m/s} = 20\, \text{kg}\cdot\text{m/s}$, giving it a velocity of $20\, \text{kg}\cdot\text{m/s} / 3.00\, \text{kg} = 6.67\, \text{m/s}$. The kinetic energy of the 3.00-kg object after the collision is $KE_{2, \text{after}} = \frac{1}{2}(3.00\, \text{kg})(6.67\, \text{m/s})^2 \approx 66.7\, \text{J}$.The total kinetic energy after the collision is $25\, \text{J} + 66.7\, \text{J} = 91.7\, \text{J}$. The kinetic energy lost during the collision is $550\, \text{J} - 91.7\, \text{J} = 458.3\, \text{J}$, which rounds to $458\, \text{J}$, making option B correct.

Question 11

Two objects,each of weight W,hang vertically by spring scales as shown in the figure.The pulleys and the strings attached to the objects have negligible weight,and there is no appreciable friction in the pulleys.The reading in each scale is 
A) W.
B) more than W, but not quite twice as much.
C) less than W.
D) 2W.
E) more than 2W.

Accepted Answer

Since the two objects are connected by a rope passing over a pulley, we know that they must be accelerating at the same rate. Therefore, the tension in the rope must be equal for both objects. Each scale is measuring the tension in the rope, which must be equal to the weight of one of the objects (since they have the same weight). Therefore, the reading in each scale is W.

Question 12

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x)= (-2.00 J∙m)/x + (4.00 J∙m²)/x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m? A) 2.13 m/s B) 3.00 m/s C) 4.68 m/s D) 3.67 m/s

Accepted Answer

We can use conservation of mechanical energy to solve this problem. The total mechanical energy of the particle is given by: E = K + U where K is the kinetic energy and U is the potential energy. At x = 1.00 m, the particle has a kinetic energy of: K = (1/2)mv^2 = (1/2)(1.00 kg)(3.00 m/s)^2 = 4.50 J and a potential energy of: U = (-2.00 J*m)/x + (4.00 J*m*²)/x² = (-2.00 J*m)/(1.00 m) + (4.00 J*m*²)/(1.00 m*²) = 2.00 J So, the total mechanical energy at x = 1.00 m is: E = K + U = 4.50 J + 2.00 J = 6.50 J At x = 5.00 m, the potential energy of the particle is: U = (-2.00 J*m)/x + (4.00 J*m*²)/x² = (-2.00 J*m)/(5.00 m) + (4.00 J*m*²)/(5.00 m*²) = 0.20 J Therefore, the kinetic energy at x = 5.00 m is: K = E - U = 6.50 J - 0.20 J = 6.30 J and the speed is: v = ²(2K/m) = ²(2(6.30 J)/(1.00 kg)) = 3.67 m/s Therefore, the answer is D, 3.67 m/s.

Question 13

Point P in the figure indicates the position of an object traveling at constant speed clockwise around the circle.Which arrow best represent the direction the object would travel if the net external force on it were suddenly reduced to zero? 
A)

B)

C) 
D)

E)

Accepted Answer

When the net external force on an object is reduced to zero, the object will continue to move in the direction of its current velocity. At point P, the object is moving upward and to the right, so it will continue moving in that direction. The arrow that best represents this direction is arrow D.

Question 14

A 2.0-kg object is moving without friction along the x-axis.The potential energy curve as a function of position is shown in the figure,and the system is conservative.If the speed of the object at the origin is 4.0 m/s,what will be its speed at 7.0 m along the +x-axis? 
A) 4.0 m/s
B) 4.2 m/s
C) 4.4 m/s
D) 4.6 m/s
E) 9.8 m/s

Accepted Answer

Conservation of mechanical energy gives us:
K1 + U1 = K2 + U2
where K1 = (1/2)mv1^2, U1 is the gravitational potential energy at the origin, K2 = (1/2)mv2^2, and U2 is the gravitational potential energy at x = 7.
At the origin, U1 = 0 since the reference level is set at x = 0.
At x = 7, U2 = -10 J
Thus,  (1/2)mv1^2 = (1/2)mv2^2 - 10 J
Simplifying and solving for v2:
v2 = sqrt(v1^2 + 20/m)
Plugging in the given values, we get:
v2 = sqrt(4^2 + 20/2) = 4.2 m/s
Therefore, the answer is B.

Question 15

Which one of the following free-body diagrams best represents the free-body diagram,with correct relative force magnitudes,of a person in an elevator that is traveling upward with an unchanging velocity? _f is the force of the floor on the person and _g is the force of gravity on the person. A) B) C) D) E)

Accepted Answer

In the elevator, the person is not accelerating, so the net force acting on the person should be zero. The only two forces acting on the person are the force of gravity downwards and the normal force (reaction force) of the floor holding the person up. Since the person is not accelerating, these two forces should be equal in magnitude and opposite in direction. Only option B represents these two forces of equal magnitude and opposite direction.

Question 16

In order to get an object moving,you must push harder on it than it pushes back on you.

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that the force you apply to an object is exactly matched by the force the object applies back on you. The object moves not because you push harder, but because you apply a force that is unbalanced by other forces acting on the object, such as friction or gravity.

Question 17

You are standing in a moving bus,facing forward,and you suddenly fall forward as the bus comes to an immediate stop.The force acting on you that causes you to fall forward is
A) the force of gravity.
B) the normal force due to your contact with the floor of the bus.
C) the force due to static friction between you and the floor of the bus.
D) the force due to kinetic friction between you and the floor of the bus.
E) No forces were acting on you to cause you to fall.

Accepted Answer

When the bus comes to an immediate stop, your body tends to continue moving forward due to inertia, not because of any external force acting on you in the forward direction. This is an example of Newton's first law of motion, which states that an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force. In this scenario, no external forward force is acting on you; you fall forward because the bus stops moving and your body tries to maintain its state of motion.

Question 18

An object is moving to the right,and experiencing a net force that is directed to the right.The magnitude of the force is decreasing with time.The speed of the object is
A) increasing.
B) decreasing.
C) constant in time.

Accepted Answer

Since the net force is directed to the right and the magnitude of the force is decreasing with time, the force is still acting in the forward direction, but its effect is decreasing. This means that the acceleration of the object is decreasing, but it is still there. Therefore, the speed of the object will be increasing at a decreasing rate, but still increasing nonetheless.

Question 19

A car is being towed at constant velocity on a horizontal road using a horizontal chain.The tension in the chain must be equal to the weight of the car in order to maintain constant velocity.

Accepted Answer

The tension in the chain must balance the frictional forces opposing the car's motion, not its weight, to maintain constant velocity. The weight of the car is counteracted by the normal force from the road.

Question 20

A fish weighing 16 N is weighed using two spring scales,each of negligible weight,as shown in the figure.What will be the readings of the scales? 
A) The bottom scale will read 16 N, and the top scale will read zero.
B) Each scale will read 16 N.
C) The top scale will read 16 N, and the bottom scale will read zero.
D) The scales will have different readings, but the sum of the two readings will be 16 N.
E) Each scale will read 8 N.

Accepted Answer

The answer of A fish weighing 16 N is weighed...

Quiz 1: A: Foundations

You swing a bat and hit a heavy box with a force of 1500 N.The force the box exerts on the bat is

A stalled car is being pushed up a hill at constant velocity by three people.The net force on the car is

Consider what happens when you jump up in the air.Which of the following is the most accurate statement?

In order to lift a bucket of concrete,you must pull up harder on the bucket than it pulls down on you.

Two weights are connected by a massless wire and pulled upward with a constant speed of 1.50 m/s by a vertical pull P.The tension in the wire is T (see figure) .Which one of the following relationships between T and P must be true?

A 615 N student standing on a scale in an elevator notices that the scale reads 645 N.From this information,the student knows that the elevator must be moving

A 20-ton truck collides with a 1500-lb car and causes a lot of damage to the car.During the collision

A 2.00-kg object traveling east at 20.0 m/s collides with a 3.00-kg object traveling west at 10.0 m/s. After the collision,the 2.00-kg object has a velocity 5.00 m/s to the west. How much kinetic energy was lost during the collision?

Two objects,each of weight W,hang vertically by spring scales as shown in the figure.The pulleys and the strings attached to the objects have negligible weight,and there is no appreciable friction in the pulleys.The reading in each scale is

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m) /x + (4.00 J∙m²) /x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

Point P in the figure indicates the position of an object traveling at constant speed clockwise around the circle.Which arrow best represent the direction the object would travel if the net external force on it were suddenly reduced to zero?

A 2.0-kg object is moving without friction along the x-axis.The potential energy curve as a function of position is shown in the figure,and the system is conservative.If the speed of the object at the origin is 4.0 m/s,what will be its speed at 7.0 m along the +x-axis?

Which one of the following free-body diagrams best represents the free-body diagram,with correct relative force magnitudes,of a person in an elevator that is traveling upward with an unchanging velocity? _f is the force of the floor on the person and _g is the force of gravity on the person.

In order to get an object moving,you must push harder on it than it pushes back on you.

You are standing in a moving bus,facing forward,and you suddenly fall forward as the bus comes to an immediate stop.The force acting on you that causes you to fall forward is

An object is moving to the right,and experiencing a net force that is directed to the right.The magnitude of the force is decreasing with time.The speed of the object is

A car is being towed at constant velocity on a horizontal road using a horizontal chain.The tension in the chain must be equal to the weight of the car in order to maintain constant velocity.

A fish weighing 16 N is weighed using two spring scales,each of negligible weight,as shown in the figure.What will be the readings of the scales?

Quiz 1: A: Foundations

You swing a bat and hit a heavy box with a force of 1500 N.The force the box exerts on the bat is

A stalled car is being pushed up a hill at constant velocity by three people.The net force on the car is

Consider what happens when you jump up in the air.Which of the following is the most accurate statement?

In order to lift a bucket of concrete,you must pull up harder on the bucket than it pulls down on you.

Two weights are connected by a massless wire and pulled upward with a constant speed of 1.50 m/s by a vertical pull P.The tension in the wire is T (see figure) .Which one of the following relationships between T and P must be true?

A 615 N student standing on a scale in an elevator notices that the scale reads 645 N.From this information,the student knows that the elevator must be moving

A 20-ton truck collides with a 1500-lb car and causes a lot of damage to the car.During the collision

A 2.00-kg object traveling east at 20.0 m/s collides with a 3.00-kg object traveling west at 10.0 m/s. After the collision,the 2.00-kg object has a velocity 5.00 m/s to the west. How much kinetic energy was lost during the collision?

Two objects,each of weight W,hang vertically by spring scales as shown in the figure.The pulleys and the strings attached to the objects have negligible weight,and there is no appreciable friction in the pulleys.The reading in each scale is

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m) /x + (4.00 J∙m2) /x2. Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

Point P in the figure indicates the position of an object traveling at constant speed clockwise around the circle.Which arrow best represent the direction the object would travel if the net external force on it were suddenly reduced to zero?

A 2.0-kg object is moving without friction along the x-axis.The potential energy curve as a function of position is shown in the figure,and the system is conservative.If the speed of the object at the origin is 4.0 m/s,what will be its speed at 7.0 m along the +x-axis?

Which one of the following free-body diagrams best represents the free-body diagram,with correct relative force magnitudes,of a person in an elevator that is traveling upward with an unchanging velocity? f is the force of the floor on the person and g is the force of gravity on the person.

In order to get an object moving,you must push harder on it than it pushes back on you.

You are standing in a moving bus,facing forward,and you suddenly fall forward as the bus comes to an immediate stop.The force acting on you that causes you to fall forward is

An object is moving to the right,and experiencing a net force that is directed to the right.The magnitude of the force is decreasing with time.The speed of the object is

A car is being towed at constant velocity on a horizontal road using a horizontal chain.The tension in the chain must be equal to the weight of the car in order to maintain constant velocity.

A fish weighing 16 N is weighed using two spring scales,each of negligible weight,as shown in the figure.What will be the readings of the scales?

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m) /x + (4.00 J∙m²) /x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

Which one of the following free-body diagrams best represents the free-body diagram,with correct relative force magnitudes,of a person in an elevator that is traveling upward with an unchanging velocity? _f is the force of the floor on the person and _g is the force of gravity on the person.