Q: A 600 kg roller coaster is at rest at the top of a 100 m hill. Assuming no energy is lost to friction, what is the total mechanical energy of the system at the top?

$$E = mgh = (600)(9.8)(100) = 588,000\ \text{J}$$

Q: A 600 kg roller coaster is launched at $$25\ \text{m/s} up a $$hill. If it comes to rest at the top and 3,000 J of energy is lost to friction, what is the maximum height $$h it $$can reach? (Use $$g = 9.8\ \text{m/s}^2)$$

$$h = \frac{\frac{1}{2}mv^2$ - 3,000}{mg} = \frac{0.5 \times 600 \times 25^2$ - 3,000}{600 \times 9.8} = 40.3\ \text{m}$$

Q: If a roller coaster has a total mechanical energy of 588,000 J at the top of a hill and 235,200 J of potential energy at a lower point, what is its kinetic energy at that point?

$$E_k = 588,000 - 235,200 = 352,800\ \text{J}$$

Q: Which equation correctly expresses the Work-Energy Theorem as applied to a roller coaster experiencing friction?

$$W_{\text{nc}} = \Delta E = E_f - E_i$$

Q: A roller coaster car of mass 600 kg is at rest at the top of a 100 m hill. What is its speed at the bottom, assuming no energy is lost to friction? ($$g = 9.8\ \text{m/s}^2)$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 100} = 44.3\ \text{m/s}$$

Question 1

According to the First Law of Thermodynamics, which of the following statements is TRUE?

Accepted Answer

Energy cannot be created or destroyed, only transferred or transformed.

Question 2

A 600 kg roller coaster is at rest at the top of a 100 m hill. Assuming no energy is lost to friction, what is the total mechanical energy of the system at the top?

Accepted Answer

$$E = mgh = (600)(9.8)(100) = 588,000\ 	ext{J}$$

Question 3

If a roller coaster loses 3,000 J of energy to friction while climbing a hill, how does this affect the total mechanical energy at the top compared to the bottom (assuming no other losses)?

Accepted Answer

The total mechanical energy at the top is 3,000 J less than at the bottom.

Question 4

A 600 kg roller coaster is launched at $$25\ 	ext{m/s} up a $$hill. If it comes to rest at the top and 3,000 J of energy is lost to friction, what is the maximum height $$h it $$can reach? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$h = \frac{\frac{1}{2}mv^2$ - 3,000}{mg} = \frac{0.5 	imes 600 	imes 25^2$ - 3,000}{600 	imes 9.8} = 40.3\ 	ext{m}$$

Question 5

Which of the following best describes the difference between energy transfer and energy transformation?

Accepted Answer

Energy transfer is moving energy between objects, while energy transformation is changing energy from one form to another.

Question 6

A roller coaster car of mass $$m$$ starts from rest at height $$h_1$$ and descends to height $$h_2. $$Neglecting friction, what is its speed $$v at$$ $$h_2$$?

Accepted Answer

$$v = \sqrt{2g(h_1$ - h_2$)}$$

Question 7

If a roller coaster has a total mechanical energy of 588,000 J at the top of a hill and 235,200 J of potential energy at a lower point, what is its kinetic energy at that point?

Accepted Answer

$$E_k = 588,000 - 235,200 = 352,800\ 	ext{J}$$

Question 8

Which equation correctly expresses the Work-Energy Theorem as applied to a roller coaster experiencing friction?

Accepted Answer

$$W_{	ext{nc}} = \Delta E = E_f - E_i$$

Question 9

A roller coaster car of mass 600 kg is at rest at the top of a 100 m hill. What is its speed at the bottom, assuming no energy is lost to friction? ($$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 100} = 44.3\ 	ext{m/s}$$

Question 10

If a roller coaster is moving at 25 m/s and comes to rest at the top of a hill after climbing, what is the change in its kinetic energy?

Accepted Answer

$$\Delta E_k = 0 - \frac{1}{2}mv^2$ = -\frac{1}{2}mv^2$

Question 11

Which of the following is an example of energy transformation in a roller coaster system?

Accepted Answer

Potential energy converting to kinetic energy as the coaster descends.

Question 12

A roller coaster loses 5,000 J of energy to sound and heat during a ride. What type of work is this energy loss associated with?

Accepted Answer

Nonconservative work

Question 13

If the total energy of a roller coaster is conserved, which of the following must be true?

Accepted Answer

The sum of kinetic and potential energy remains constant, ignoring nonconservative forces.

Question 14

A roller coaster car has 352,800 J of kinetic energy and 235,200 J of potential energy at a certain point. What is its total mechanical energy?

Accepted Answer

$$E_{	ext{total}} = 352,800 + 235,200 = 588,000\ 	ext{J}$$

Question 15

Which of the following best describes a scenario where energy is transferred but not transformed?

Accepted Answer

A hot object warming a cooler object by direct contact.

Question 16

If a roller coaster starts at rest at a height of 50 m and reaches a speed of 31.3 m/s at the bottom, what principle explains this result?

Accepted Answer

Conservation of mechanical energy

Question 17

A roller coaster car of mass 600 kg is moving at 20 m/s at the bottom of a hill. How much work must be done by friction to bring it to rest at the top of a 30 m hill? ($$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$W = \left[\frac{1}{2}mv^2$ - mghight] = [0.5 	imes 600 	imes 20^2$ - 600 	imes 9.8 	imes 30] = 120,000 - 176,400 = -56,400\ 	ext{J}$$

Question 18

Which of the following is NOT a form of energy loss in a real roller coaster system?

Accepted Answer

Increase in gravitational potential energy

Question 19

A roller coaster car is at rest at the top of a hill and then descends. Which of the following best describes the energy changes as it moves down?

Accepted Answer

Potential energy decreases while kinetic energy increases.

Conservation of Energy and the First Law of Thermodynamics in Roller Coaster Physics

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