Q: A 2 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is the speed of the ball just before it hits the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14\ \mathrm{m/s}$$

Q: A hiker climbs from the shore of a lake to the top of a mountain, increasing her gravitational potential energy by $$5000\ \mathrm{J}. If $$her mass is $$50\ \mathrm{kg}$$, what is the change in her elevation? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$\Delta y = \frac{\Delta U}{mg} = \frac{5000}{50 \times 9.8} = 10.2\ \mathrm{m}$$

Q: A 0.5 kg mass is attached to a spring with $$k = 200\ \mathrm{N/m}$$ and is compressed $$0.1\ \mathrm{m}$$ from equilibrium. What is the elastic potential energy stored in the spring?

$$U_{el} = \frac{1}{2}kx^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \mathrm{J}$$

Question 1

A 2 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is the speed of the ball just before it hits the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14\ \mathrm{m/s}$$

Question 2

Which of the following statements about conservative forces is TRUE?

Accepted Answer

The work done by a conservative force depends only on the initial and final positions, not on the path taken.

Question 3

A block of mass $$m is $$attached to a spring with force constant $$k$$ and is pulled a distance $$x$$ from equilibrium and released from rest. What is the maximum speed of the block?

Accepted Answer

$$v_{max} = \sqrt{\frac{k}{m}}x$$

Question 4

A hiker climbs from the shore of a lake to the top of a mountain, increasing her gravitational potential energy by $$5000\ \mathrm{J}. If $$her mass is $$50\ \mathrm{kg}$$, what is the change in her elevation? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta y = \frac{\Delta U}{mg} = \frac{5000}{50 	imes 9.8} = 10.2\ \mathrm{m}$$

Question 5

Which of the following is NOT a property of a conservative force?

Accepted Answer

The work done depends on the path taken between two points.

Question 6

A 0.5 kg mass is attached to a spring with $$k = 200\ \mathrm{N/m}$$ and is compressed $$0.1\ \mathrm{m}$$ from equilibrium. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U_{el} = \frac{1}{2}kx^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ \mathrm{J}$$

Question 7

A ball is thrown vertically upward with an initial speed $$v_0$$ from ground level. Ignoring air resistance, at what height will the ball's kinetic energy be half its initial value?

Accepted Answer

$$h = \frac{v_0$^2}{4g}$$

Question 8

Which of the following best describes the energy transformation in a car tire as it rolls and flexes on the road?

Accepted Answer

Mechanical energy is converted to internal energy due to nonconservative friction forces.

Question 9

A block slides down a frictionless curved ramp from height $$h. $$Which of the following statements is correct about the work done by gravity?

Accepted Answer

The work done by gravity depends only on the vertical displacement, not the path taken.

Question 10

Which equation correctly expresses the law of conservation of energy when nonconservative forces are present?

Accepted Answer

$$\Delta K + \Delta U + \Delta U_{int} = 0$$

Question 11

A glider attached to a spring oscillates on a frictionless air track. At the point where the potential energy is at a minimum, what can be said about the force and the equilibrium?

Accepted Answer

The force is zero and the system is in stable equilibrium.

Question 12

Given the potential energy function $$U(x) = \frac{1}{2}kx^2$, what is the corresponding force F(x$$)$$?

Accepted Answer

$$F(x) = -kx$$

Question 13

A 1 kg mass is dropped from rest from a height of 5 m onto a spring with $$k = 100\ \mathrm{N/m}. $$What is the maximum compression $$x of $$the spring? (Ignore air resistance and take $$g = 10\ \mathrm{m/s^2$})$$

Accepted Answer

$$x = \sqrt{\frac{2mg h}{k}} = \sqrt{\frac{2 	imes 1 	imes 10 	imes 5}{100}} = 1\ \mathrm{m}$$

Question 14

Which of the following is TRUE about energy diagrams for a particle in a potential $$U(x)$$?

Accepted Answer

The particle can only move in regions where its total energy $$E is $$greater than or equal to $$U(x).$$

Question 15

Which mathematical operation gives the force from a potential energy function $$U(x, y, z) in $$three dimensions?

Accepted Answer

$$\vec{F} = -
abla U$$

Question 16

A gymnast balances on one hand at the top of a narrow beam. What type of equilibrium is she in, and why?

Accepted Answer

Unstable equilibrium, because any small displacement lowers her potential energy and she will fall further.

Question 17

A block slides down a rough incline and comes to rest. Which statement best describes the energy transformation?

Accepted Answer

Mechanical energy is transformed into internal energy due to friction.

Question 18

If the slope of the potential energy function $$U(x) is $$zero at $$x_0$$, what does this imply about the force and equilibrium at $$x_0$$?

Accepted Answer

The force is zero and $$x_0 is a $$point of equilibrium.

Potential Energy and Energy Conservation – Study Notes

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