Question 1

Which,if any,of the following statements concerning the work done by a conservative force is NOT true?

Accepted Answer

All the statements provided are true characteristics of a conservative force. Conservative forces, such as gravity or spring forces, have the property that the work done is independent of the path taken, depends only on the initial and final positions, and is zero if the starting and ending points are the same.

Question 2

Block 1 and block 2 have the same mass,m,and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction,respectively.If the coefficient of friction is the same in both cases,which of the blocks is going faster when it reaches the bottom of its respective incline?

Accepted Answer

Block 2 is faster because it travels down a steeper incline, resulting in a greater component of gravitational force along the incline and less time for friction to act, leading to a higher final speed.

Question 3

Is it possible for a system to have negative potential energy?

Accepted Answer

The potential energy of a system is defined as the work that is done by external forces to bring the system from a reference state to its current state. The choice of the zero of potential energy is arbitrary, and therefore, it is possible for a system to have negative potential energy. This is because the zero of potential energy can be chosen in such a way that the potential energy of the system is negative. The kinetic energy of the system is independent of the choice of the zero of potential energy and can be positive, negative, or zero. Therefore, options A and D are incorrect. The total energy of the system can be positive, negative, or zero, depending on the kinetic and potential energies of the system, and is not a sufficient condition for the system to have negative potential energy. Therefore, option B is also incorrect. Option E is incorrect as well because negative potential energy can have physical meaning, such as in the case of a gravitational potential energy below the surface of the Earth.

Question 4

The plot in the figure shows the potential energy of a particle,due to the force exerted on it by another particle,as a function of distance.At which of the three points labeled in the figure is the magnitude of the force on the particle greatest?

Accepted Answer

The magnitude of force is given by the negative slope of the potential energy curve. At point X, the slope is the steepest, indicating the largest magnitude of force. At point Y and Z, the slope is less steep, indicating a smaller magnitude of force.

Question 5

A ball drops some distance and gains 30 J of kinetic energy.Do NOT ignore air resistance.How much gravitational potential energy did the ball lose?

Accepted Answer

When the ball drops, it loses gravitational potential energy and gains kinetic energy. The gain in kinetic energy is 30 J, but due to air resistance, some of the energy is lost to the surroundings. This means that the loss in gravitational potential energy is more than 30 J. Therefore, the correct choice is A) more than 30 J.

Question 6

A ball drops some distance and loses 30 J of gravitational potential energy.Do NOT ignore air resistance.How much kinetic energy did the ball gain?

Accepted Answer

Due to air resistance, some of the gravitational potential energy is converted into other forms of energy, such as thermal energy and sound energy, rather than into kinetic energy. Therefore, the amount of kinetic energy gained by the ball will be less than the amount of gravitational potential energy lost.

Question 7

Swimmers at a water park have a choice of two frictionless water slides as shown in the figure.Although both slides drop over the same height,h,slide 1 is straight while slide 2 is curved,dropping quickly at first and then leveling out.How does the speed v₁ of a swimmer reaching the end of slide 1 compares with v₂,the speed of a swimmer reaching the end of slide 2?

Accepted Answer

The answer of Swimmers at a water park have a...

Question 8

A box of mass m is pressed against (but is not attached to)an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment with a box of mass 2m

Accepted Answer

The answer of A box of mass m is pressed...

Question 9

A potential energy function for system 1 is given by U₁(x)= Cx² + Bx³.The potential energy function for system 2 is given by U₂(x)= A + Cx² + Bx³,where A is a positive quantity.How does the force on system 1 relate to the force on system 2 at a given position?

Accepted Answer

The force on both systems is given by the negative gradient of their respective potential energy functions. Therefore, the force depends only on x and not on the parameters C, B, A of the potential energy functions. Since the two systems have the same potential energy function except for the constant term A in the second system, their forces will be identical.

Question 10

Two stones,one of mass m and the other of mass 2m,are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance.Which statement about these stones is true?

Accepted Answer

The answer of Two stones,one of mass m and the...

Question 11

A box of mass m is pressed against (but is not attached to)an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment but instead compress the spring a distance of 2x

Accepted Answer

The answer of A box of mass m is pressed...

Question 12

An athlete stretches a spring an extra 40.0 cm beyond its initial length.How much energy has he transferred to the spring,if the spring constant is 52.9 N/cm?

Accepted Answer

The energy transferred to the spring can be calculated using the formula for the potential energy stored in a spring: $E = \frac{1}{2}kx^2$, where $E$ is the energy in joules, $k$ is the spring constant in N/m, and $x$ is the displacement in meters. Given $k = 52.9 \, \text{N/cm} = 5290 \, \text{N/m}$ (since $1 \, \text{N/cm} = 100 \, \text{N/m}$) and $x = 40.0 \, \text{cm} = 0.4 \, \text{m}$, the energy transferred is $E = \frac{1}{2} \times 5290 \times (0.4)^2 = 423 \, \text{J}$.

Question 13

It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure.What is the length s of the ramp from A to B?

Accepted Answer

The answer of It requires 6.0 J of work is...

Question 14

A tennis ball bounces on the floor three times.If each time it loses 22.0% of its energy due to heating,how high does it rise after the third bounce,provided we released it  from the floor?

Accepted Answer

The answer of A tennis ball bounces on the floor...

Question 15

When an object is solely under the influence of conservative forces,the sum of its kinetic and potential energies does not change.

Accepted Answer

This statement is a restatement of the Law of Conservation of Energy, which states that in a closed system, energy is conserved and cannot be created or destroyed, only transferred or transformed from one form to another. Conservative forces, such as gravity or electrostatic forces, conserve mechanical energy, which is the sum of potential and kinetic energy. Therefore, if an object is only under the influence of conservative forces, the total mechanical energy of the object remains constant.

Question 16

Two identical balls are thrown directly upward,ball A at speed v and ball B at speed 2v,and they feel no air resistance.Which statement about these balls is correct?

Accepted Answer

The height reached by an object thrown upward is proportional to the square of its initial velocity. Since kinetic energy is proportional to the square of the velocity ($KE = \frac{1}{2}mv^2$), doubling the initial speed ($2v$) results in four times the initial kinetic energy ($4 \times \frac{1}{2}mv^2 = 2mv^2$). This increased energy allows the object to reach a height four times greater than if it were thrown at speed $v$, assuming no air resistance and constant acceleration due to gravity.

Question 17

A box of mass m is pressed against (but is not attached to)an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment but instead use a spring having force constant 2k

Accepted Answer

According to the conservation of energy,
Initial potential energy of the spring = Final kinetic energy of the box
1/2 kx² = 1/2 mv²
If the spring constant is doubled, then the new potential energy of the spring is
1/2 (2k)x² = 2(1/2 kx²) = 2 times the initial potential energy.
Therefore, when the box is released, it will have twice the initial kinetic energy and will move up the incline to a new height h'.
1/2 (2k)x² = 1/2 mv² + mgh'
On solving for h', we get
h' = 2x
As the box moves up to a height twice the initial height, its speed will be given by,
v' = √(2gh') = √(2g(2x)) = 11ea83ea_699f_884f_aeff_f1072fcdf62d_TB6394_11 times the initial velocity.

Question 18

An 8.0-kg block is released from rest,with v₁ = 0.00 m/s,on a rough incline,as shown in the figure.The block moves a distance of 1.6-m down the incline,in a time interval of 0.80 s,and acquires a velocity of v₂ = 4.0 m/s.How much work does gravity do on the block during this process?

Accepted Answer

The answer of An 8.0-kg block is released from rest,with...

Question 19

A girl throws a stone from a bridge.Consider the following ways she might throw the stone.The speed of the stone as it leaves her hand is the same in each case,and air resistance is negligible. Case A: Thrown straight up.
Case B: Thrown straight down.
Case C: Thrown out at an angle of 45° above horizontal.
Case D: Thrown straight out horizontally.
In which case will the speed of the stone be greatest when it hits the water below?

Accepted Answer

In the absence of air resistance, all objects near the Earth's surface accelerate downwards at the same rate regardless of their initial motion. This means that the final speed of the stone when it hits the water depends only on the height from which it is dropped and not on the direction in which it is thrown. Therefore, the speed will be the same in all cases when the stone hits the water.

Question 20

You do 174 J of work while pulling your sister back on a swing,whose chain is 5.10 m long.You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest.What is your sister's mass,assuming negligible friction?

Accepted Answer

The work done is equal to the change in gravitational potential energy, which is mgh. The height (h) can be found using trigonometry: h = L - Lcos(θ), where L is the length of the chain. Solving for mass (m) using the work-energy principle gives m = W / (g * h), where W is the work done and g is the acceleration due to gravity (9.8 m/s²). Plugging in the values gives approximately 22.9 kg.

Quiz 7: Potential Energy and Energy Conservation

Which,if any,of the following statements concerning the work done by a conservative force is NOT true?

Is it possible for a system to have negative potential energy?

The plot in the figure shows the potential energy of a particle,due to the force exerted on it by another particle,as a function of distance.At which of the three points labeled in the figure is the magnitude of the force on the particle greatest?

A ball drops some distance and gains 30 J of kinetic energy.Do NOT ignore air resistance.How much gravitational potential energy did the ball lose?

A ball drops some distance and loses 30 J of gravitational potential energy.Do NOT ignore air resistance.How much kinetic energy did the ball gain?

A potential energy function for system 1 is given by U₁(x) = Cx² + Bx³.The potential energy function for system 2 is given by U₂(x) = A + Cx² + Bx³,where A is a positive quantity.How does the force on system 1 relate to the force on system 2 at a given position?

Two stones,one of mass m and the other of mass 2m,are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance.Which statement about these stones is true?

An athlete stretches a spring an extra 40.0 cm beyond its initial length.How much energy has he transferred to the spring,if the spring constant is 52.9 N/cm?

It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure.What is the length s of the ramp from A to B?

A tennis ball bounces on the floor three times.If each time it loses 22.0% of its energy due to heating,how high does it rise after the third bounce,provided we released it from the floor?

When an object is solely under the influence of conservative forces,the sum of its kinetic and potential energies does not change.

Two identical balls are thrown directly upward,ball A at speed v and ball B at speed 2v,and they feel no air resistance.Which statement about these balls is correct?

An 8.0-kg block is released from rest,with v₁ = 0.00 m/s,on a rough incline,as shown in the figure.The block moves a distance of 1.6-m down the incline,in a time interval of 0.80 s,and acquires a velocity of v₂ = 4.0 m/s.How much work does gravity do on the block during this process?

You do 174 J of work while pulling your sister back on a swing,whose chain is 5.10 m long.You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest.What is your sister's mass,assuming negligible friction?

Quiz 7: Potential Energy and Energy Conservation

Which,if any,of the following statements concerning the work done by a conservative force is NOT true?

Is it possible for a system to have negative potential energy?

The plot in the figure shows the potential energy of a particle,due to the force exerted on it by another particle,as a function of distance.At which of the three points labeled in the figure is the magnitude of the force on the particle greatest?

A ball drops some distance and gains 30 J of kinetic energy.Do NOT ignore air resistance.How much gravitational potential energy did the ball lose?

A ball drops some distance and loses 30 J of gravitational potential energy.Do NOT ignore air resistance.How much kinetic energy did the ball gain?

A potential energy function for system 1 is given by U1(x) = Cx2 + Bx3.The potential energy function for system 2 is given by U2(x) = A + Cx2 + Bx3,where A is a positive quantity.How does the force on system 1 relate to the force on system 2 at a given position?

Two stones,one of mass m and the other of mass 2m,are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance.Which statement about these stones is true?

An athlete stretches a spring an extra 40.0 cm beyond its initial length.How much energy has he transferred to the spring,if the spring constant is 52.9 N/cm?

It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure.What is the length s of the ramp from A to B?

A tennis ball bounces on the floor three times.If each time it loses 22.0% of its energy due to heating,how high does it rise after the third bounce,provided we released it from the floor?

When an object is solely under the influence of conservative forces,the sum of its kinetic and potential energies does not change.

Two identical balls are thrown directly upward,ball A at speed v and ball B at speed 2v,and they feel no air resistance.Which statement about these balls is correct?

An 8.0-kg block is released from rest,with v1 = 0.00 m/s,on a rough incline,as shown in the figure.The block moves a distance of 1.6-m down the incline,in a time interval of 0.80 s,and acquires a velocity of v2 = 4.0 m/s.How much work does gravity do on the block during this process?

You do 174 J of work while pulling your sister back on a swing,whose chain is 5.10 m long.You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest.What is your sister's mass,assuming negligible friction?

A potential energy function for system 1 is given by U₁(x) = Cx² + Bx³.The potential energy function for system 2 is given by U₂(x) = A + Cx² + Bx³,where A is a positive quantity.How does the force on system 1 relate to the force on system 2 at a given position?

An 8.0-kg block is released from rest,with v₁ = 0.00 m/s,on a rough incline,as shown in the figure.The block moves a distance of 1.6-m down the incline,in a time interval of 0.80 s,and acquires a velocity of v₂ = 4.0 m/s.How much work does gravity do on the block during this process?