Question 1

Susana ascends a mountain via a short, steep trail. Sean ascends the same mountain via a long, gentle trail. Which of the following statements is true?
A) Susana gains more gravitational potential energy than Sean.
B) Susana gains less gravitational potential energy than Sean.
C) Susana gains the same gravitational potential energy as Sean.
D) To compare energies, we must know the height of the mountain.
E) To compare energies, we must know the lengths of the two trails.

Accepted Answer

Susana and Sean both ascend the same mountain, which means they reach the same height above the base level. Gravitational potential energy depends on the height gained and the mass of the object, not the path taken to reach that height. Since they reach the same height, they gain the same amount of gravitational potential energy, regardless of the steepness or length of their respective trails.

Question 2

The reference point for gravitational potential energy
A) must be at the initial position of the object.
B) must be at the final position of the object.
C) must be at ground level.
D) must be at the lowest position ever reached by the object.
E) can be chosen arbitrarily.

Accepted Answer

The reference point for gravitational potential energy can be chosen arbitrarily, as long as it is consistent throughout the problem. For example, it could be chosen to be ground level, the lowest position ever reached by the object, or any other convenient location.

Question 3

Which potential energy versus displacement curve best represents that of an extended spring? 
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

C

Question 4

When the potential energy U(r) is given as in Figure A, then the force is given in Figure B by curve
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

The answer of  When the potential energy U(r) is...

Question 5

Calculate the work done by a force, , around a closed path, first going from P₁ (1,1) to P₂ (4,4) along path a and returning along path b. A) 0 J B) 3 J C) 7 J D) 13 J E) 17 J

Accepted Answer

Since the force is being moved around a closed path, the work done by the force should be 0 J according to the work-energy principle. Therefore, the answer is A) 0 J.

Question 6

A block with a mass M = 4.85 kg is resting on a slide that has a curved surface. There is no friction. The speed of the block after it has slid along the slide sufficiently far for its vertical drop to be 19.6 m is
A) 19.6 m/s
B) 384 m/s
C) 73 m/s
D) 43.2 m/s
E) The problem cannot be solved because the shape of the curved slide is not given.

Accepted Answer

The speed of the block can be found using the conservation of energy principle, where the potential energy at the top is converted into kinetic energy at the bottom. The formula for this is $v = \sqrt{2gh}$, where $g = 9.8 \, \text{m/s}^2$ and $h = 19.6 \, \text{m}$. Plugging in these values gives $v = \sqrt{2 \times 9.8 \times 19.6} = 19.6 \, \text{m/s}$.

Question 7

The potential energy function for a conservative force acting in the x direction on a particle is shown below. The number of points where the net force on the particle is equal to zero are 
A) B and D.
B) C and E.
C) B, C, D, and E.
D) A and F.
E) any point between C and D.

Accepted Answer

The net force acting on a particle is given by the negative gradient of the potential energy function. In this case, the potential energy function has a minimum at point C and a maximum at point D, and zero slope at points B and E. Therefore, the net force is zero at points B, C, D, and E. The net force is not zero at points A and F, as the slope is non-zero at these points. Therefore, the correct choice is C.

Question 8

A 5200-kg cable car in Hong Kong is pulled a distance of 360 m up a hill inclined at 12º from the horizontal. The change in the potential energy of the car is A) 1.8 $\times$ 10⁷ J B) 1.2 $\times$ 10⁷ J C) 3.8 $\times$ 10⁶ J D) 6.0 $\times$ 10⁷ J E) 1.8 $\times$ 10⁶ J

Accepted Answer

The answer of A 5200-kg cable car in Hong Kong...

Question 9

Which of the following statements is true?
A) Friction is a conservative force and does negative work.
B) Potential energy may be defined by the equation U(x) = -dF(x)/dx
C) The work done by a conservative force between two points depends on the path taken between those points.
D) A conservative force cannot change a body's total energy.
E) The work done by a conservative force while a body moves at constant velocity must be zero.

Accepted Answer

The answer of Which of the following statements is true?
A)...

Question 10

A woman runs up a flight of stairs. The gain in her gravitational potential energy is U. If she runs up the same stairs with twice the speed, what is her gain in potential energy?
A) U
B) 2U
C)  U
D) 4U
E)  U

Accepted Answer

The answer of A woman runs up a flight of...

Question 11

The graph shows a plot of the gravitational potential energy U of a 1-kg body as a function of its height h above the surface of a planet. The acceleration due to gravity at the surface of the planet is A) 0 m/s² B) 9.8 m/s² C) 6.0 m/s² D) 3.0 m/s² E) None of these is correct.

Accepted Answer

The answer of  The graph shows a plot of...

Question 12

A block of mass m starts from position 1 and moves up a frictionless inclined plane with an initial speed v. At some later time the block has moved down the plane and at position 2 has a speed u. If a and b are the heights above the bottom of the plane, the magnitude of u can be determined from A) u² = v² - 2g(a - b) B) u² = v² + 2g(a + b) C) u² = v² + 2g(a - b) D) u² = v² + 2g(b - a) E) u² = v² + g(a - b)

Accepted Answer

The conservation of energy principle can be applied to the motion of the block. The initial kinetic energy of the block equals the sum of the potential and kinetic energy when it reaches position 2. Using this principle, we can write:

1/2 mv^2 = mgh + 1/2 mu^2

where h = a - b is the height difference between positions 1 and 2.

Simplifying this equation, we get:

u^2 = v^2 + 2gh

Substituting h = a - b, we get:

u^2 = v^2 + 2g(a - b)

Taking the square root of both sides, we get:

u = sqrt(v^2 + 2g(a - b))

Therefore, the correct answer is C.

Question 13

Which of the following statements is NOT correct?
A) The work done by a conservative force on an object is independent on the path taken.
B) The work done by a conservative force on an object along path A$\to$B is negative that of path B$\to$A.
C) The force due to gravity is an example of a conservative force.
D) Friction is an example of a conservative force.
E) The work done by friction on an object depends on the path taken.

Accepted Answer

Friction is an example of a non-conservative force, as the work done by friction on an object depends on the path taken. The other statements are all correct.

Question 14

A spring with force constant k = 300 N/m is compressed 9.0 cm. What is the potential energy in the spring? A) 1.2 $\times$ 10⁴ J B) 2.4 J C) 2.7 $\times$ 10⁴ J D) 27 J E) 1.2 J

Accepted Answer

The potential energy stored in a compressed spring is given by the formula $ \frac{1}{2}kx^2 $, where $ k $ is the spring constant and $ x $ is the compression distance. Here, $ k = 300 \, \text{N/m} $ and $ x = 9.0 \, \text{cm} = 0.09 \, \text{m} $. Plugging these values into the formula gives $ \frac{1}{2} \times 300 \times (0.09)^2 = 1.215 \, \text{J} $, which rounds to 1.2 J.

Question 15

The potential energy function for a conservative force acting in the x direction is shown in the figure on the right. Where would the particle experience a force directed to the right? 
A) between A & B and E & F
B) between B & C and C & D
C) between B & C and D & E
D) at points B and D
E) at points C and E

Accepted Answer

The answer of The potential energy function for a conservative...

Question 16

According to Quantum Chromodynamics, the force that keeps quarks confined within a proton (or neutron) increases as the separation between the individual quarks increases. Which statement below best represents this scenario? A) The quarks are tied together by nonstretchable strings. B) The quarks are tied together by elastic strings. C) The quarks move independently of each other. D) The force between the quarks has a 1/r² behavior like gravity. E) The potential energy of a quark decreases with separation.

Accepted Answer

According to Quantum Chromodynamics (QCD), the force that keeps quarks confined within a proton (or neutron) increases as the separation between the individual quarks increases. This is similar to stretching an elastic band, where the force required to pull the band increases as it stretches. Therefore, option B, "The quarks are tied together by elastic strings," best represents this scenario. Option A is incorrect as there is no evidence to suggest that the strings are non-stretchable. Option C is incorrect as quarks are bound together within a proton (or neutron), and do not move independently of each other. Option D is incorrect as the strong force, which binds quarks together, has a completely different functional form compared to the gravitational force. Option E is also incorrect as the potential energy of a quark actually increases with separation, due to the increased force required to keep them bound together.

Question 17

In magazine car tests an important indicator of performance is the zero to 60 mph (0 to 96.6 km/h) acceleration time. A time below 6 s is considered to be extremely quick. If a car with mass 1300 kg were dropped vertically from a great height, how long would it take to go from zero to 60 mph and what would the magnitude of the change in gravitational potential energy be during this time? (neglect air resistance)
A) 2.74 s and 17.4 kJ
B) 2.74 s and 468 kJ
C) 2.74 s and 468 MJ
D) 0.37 s and 468 MJ
E) 2.74 s and 17.4 MJ

Accepted Answer

The answer of In magazine car tests an important indicator...

Question 18

Calculate the work done by a force, , along the path (0,0) $\to$P₁ (2,0) $\to$ P₂ (2,2). A) 2 J B) 4 J C) 6 J D) 8 J E) 10 J

Accepted Answer

The answer of Calculate the work done by a force,...

Question 19

Which of the following statements is true?
A) The kinetic and potential energies of an object must always be positive quantities.
B) The kinetic and potential energies of an object must always be negative quantities.
C) Kinetic energy can be negative but potential energy cannot.
D) Potential energy can be negative but kinetic energy cannot.
E) None of these statements is true.

Accepted Answer

Kinetic energy, defined as $ \frac{1}{2}mv^2 $ (where $ m $ is mass and $ v $ is velocity), is always positive because mass and the square of velocity are always positive. Potential energy, however, can be negative depending on the reference point chosen. For example, in gravitational potential energy calculations, the potential energy can be negative if the reference point is chosen to be at a position higher than the object's position.

Question 20

A 75-kg man climbs the stairs to the fifth floor of a building, a total height of 16 m. His potential energy has increased by A) 1.2 $\times$ 10⁴ J B) 5.9 $\times$ 10⁴ J C) 4.7 $\times$ 10⁴ J D) 3.8 $\times$ 10⁴ J E) 5.9 $\times$ 10³ J

Accepted Answer

The answer of A 75-kg man climbs the stairs to...

Quiz 7: Conservation of Energy

Susana ascends a mountain via a short, steep trail. Sean ascends the same mountain via a long, gentle trail. Which of the following statements is true?

The reference point for gravitational potential energy

Which potential energy versus displacement curve best represents that of an extended spring?

When the potential energy U(r) is given as in Figure A, then the force is given in Figure B by curve

Calculate the work done by a force, , around a closed path, first going from P1 (1,1) to P2 (4,4) along path a and returning along path b.

A block with a mass M = 4.85 kg is resting on a slide that has a curved surface. There is no friction. The speed of the block after it has slid along the slide sufficiently far for its vertical drop to be 19.6 m is

The potential energy function for a conservative force acting in the x direction on a particle is shown below. The number of points where the net force on the particle is equal to zero are

A 5200-kg cable car in Hong Kong is pulled a distance of 360 m up a hill inclined at 12º from the horizontal. The change in the potential energy of the car is

Which of the following statements is true?

A woman runs up a flight of stairs. The gain in her gravitational potential energy is U. If she runs up the same stairs with twice the speed, what is her gain in potential energy?

The graph shows a plot of the gravitational potential energy U of a 1-kg body as a function of its height h above the surface of a planet. The acceleration due to gravity at the surface of the planet is

A block of mass m starts from position 1 and moves up a frictionless inclined plane with an initial speed v. At some later time the block has moved down the plane and at position 2 has a speed u. If a and b are the heights above the bottom of the plane, the magnitude of u can be determined from

Which of the following statements is NOT correct?

A spring with force constant k = 300 N/m is compressed 9.0 cm. What is the potential energy in the spring?

The potential energy function for a conservative force acting in the x direction is shown in the figure on the right. Where would the particle experience a force directed to the right?

According to Quantum Chromodynamics, the force that keeps quarks confined within a proton (or neutron) increases as the separation between the individual quarks increases. Which statement below best represents this scenario?

Calculate the work done by a force, , along the path (0,0) →\to→ P1 (2,0) →\to→ P2 (2,2) .

Which of the following statements is true?

A 75-kg man climbs the stairs to the fifth floor of a building, a total height of 16 m. His potential energy has increased by

Calculate the work done by a force, , around a closed path, first going from P₁ (1,1) to P₂ (4,4) along path a and returning along path b.