Worksheet titled "Kinetic and Potential Energy Worksheet" featuring problems to determine and calculate kinetic and gravitational potential energy using given formulas.

Kinetic and Potential Energy Worksheet Solution

The worksheet asks you to determine whether the objects in the problems have kinetic energy (KE) or gravitational potential energy (GPE), choose the correct formula, and calculate the energy. Here's a step-by-step solution for each problem:

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#### Formulas:
1. Kinetic Energy (KE):
\[
KE = \frac{1}{2}mv^2
\]
- \( m \) is the mass of the object (in kg).
- \( v \) is the velocity of the object (in m/s).

2. Gravitational Potential Energy (GPE):
\[
GPE = mgh
\]
- \( m \) is the mass of the object (in kg).
- \( g \) is the acceleration due to gravity (\( 9.8 \, \text{m/s}^2 \)).
- \( h \) is the height above the reference point (in meters).

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Problem 1:

You serve a volleyball with a mass of 2.1 kg. The ball leaves your hand with a speed of 30 m/s. The ball has ________ energy. Calculate it.

- Type of Energy: The ball is moving, so it has kinetic energy (KE).
- Formula: \( KE = \frac{1}{2}mv^2 \)
- Given:
- \( m = 2.1 \, \text{kg} \)
- \( v = 30 \, \text{m/s} \)

Calculation:
\[
KE = \frac{1}{2} \times 2.1 \times (30)^2
\]
\[
KE = \frac{1}{2} \times 2.1 \times 900
\]
\[
KE = 1.05 \times 900
\]
\[
KE = 945 \, \text{J}
\]

Answer: The ball has kinetic energy, and \( KE = 945 \, \text{J} \).

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Problem 2:

A baby carriage is sitting at the top of a hill that is 21 m high. The carriage with the baby weighs 12 N. The carriage has ________ energy. Calculate it.

- Type of Energy: The carriage is stationary but elevated, so it has gravitational potential energy (GPE).
- Formula: \( GPE = mgh \)
- Given:
- Weight (\( W \)) = 12 N
- \( h = 21 \, \text{m} \)
- \( g = 9.8 \, \text{m/s}^2 \)

Step 1: Find the mass (\( m \)) using the weight formula \( W = mg \):
\[
m = \frac{W}{g} = \frac{12}{9.8} \approx 1.224 \, \text{kg}
\]

Step 2: Calculate GPE:
\[
GPE = mgh = 1.224 \times 9.8 \times 21
\]
\[
GPE = 1.224 \times 205.8
\]
\[
GPE \approx 251.7 \, \text{J}
\]

Answer: The carriage has gravitational potential energy, and \( GPE \approx 251.7 \, \text{J} \).

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Problem 3:

A car is traveling with a velocity of 40 m/s and has a mass of 1120 kg. The car has ________ energy. Calculate it.

- Type of Energy: The car is moving, so it has kinetic energy (KE).
- Formula: \( KE = \frac{1}{2}mv^2 \)
- Given:
- \( m = 1120 \, \text{kg} \)
- \( v = 40 \, \text{m/s} \)

Calculation:
\[
KE = \frac{1}{2} \times 1120 \times (40)^2
\]
\[
KE = \frac{1}{2} \times 1120 \times 1600
\]
\[
KE = 560 \times 1600
\]
\[
KE = 896,000 \, \text{J}
\]

Answer: The car has kinetic energy, and \( KE = 896,000 \, \text{J} \).

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Problem 4:

A cinder block is sitting on a platform 20 m high. It weighs 79 N. The block has ________ energy. Calculate it.

- Type of Energy: The block is stationary but elevated, so it has gravitational potential energy (GPE).
- Formula: \( GPE = mgh \)
- Given:
- Weight (\( W \)) = 79 N
- \( h = 20 \, \text{m} \)
- \( g = 9.8 \, \text{m/s}^2 \)

Step 1: Find the mass (\( m \)) using the weight formula \( W = mg \):
\[
m = \frac{W}{g} = \frac{79}{9.8} \approx 8.061 \, \text{kg}
\]

Step 2: Calculate GPE:
\[
GPE = mgh = 8.061 \times 9.8 \times 20
\]
\[
GPE = 8.061 \times 196
\]
\[
GPE \approx 1578.1 \, \text{J}
\]

Answer: The block has gravitational potential energy, and \( GPE \approx 1578.1 \, \text{J} \).

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Problem 5:

There is a bell at the top of a tower that is 45 m high. The bell weighs 190 N. The bell has ________ energy. Calculate it.

- Type of Energy: The bell is stationary but elevated, so it has gravitational potential energy (GPE).
- Formula: \( GPE = mgh \)
- Given:
- Weight (\( W \)) = 190 N
- \( h = 45 \, \text{m} \)
- \( g = 9.8 \, \text{m/s}^2 \)

Step 1: Find the mass (\( m \)) using the weight formula \( W = mg \):
\[
m = \frac{W}{g} = \frac{190}{9.8} \approx 19.388 \, \text{kg}
\]

Step 2: Calculate GPE:
\[
GPE = mgh = 19.388 \times 9.8 \times 45
\]
\[
GPE = 19.388 \times 441
\]
\[
GPE \approx 8560.7 \, \text{J}
\]

Answer: The bell has gravitational potential energy, and \( GPE \approx 8560.7 \, \text{J} \).

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Problem 6:

A roller coaster is at the top of a 72 m hill and weighs 966 N. The coaster (at this moment) has ________ energy. Calculate it.

- Type of Energy: The roller coaster is stationary but elevated, so it has gravitational potential energy (GPE).
- Formula: \( GPE = mgh \)
- Given:
- Weight (\( W \)) = 966 N
- \( h = 72 \, \text{m} \)
- \( g = 9.8 \, \text{m/s}^2 \)

Step 1: Find the mass (\( m \)) using the weight formula \( W = mg \):
\[
m = \frac{W}{g} = \frac{966}{9.8} \approx 98.571 \, \text{kg}
\]

Step 2: Calculate GPE:
\[
GPE = mgh = 98.571 \times 9.8 \times 72
\]
\[
GPE = 98.571 \times 705.6
\]
\[
GPE \approx 69,500.7 \, \text{J}
\]

Answer: The roller coaster has gravitational potential energy, and \( GPE \approx 69,500.7 \, \text{J} \).

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Problem 7:

If a 25 kg object is moving at a velocity of 5 m/s, the object has ________ energy. Calculate it.

- Type of Energy: The object is moving, so it has kinetic energy (KE).
- Formula: \( KE = \frac{1}{2}mv^2 \)
- Given:
- \( m = 25 \, \text{kg} \)
- \( v = 5 \, \text{m/s} \)

Calculation:
\[
KE = \frac{1}{2} \times 25 \times (5)^2
\]
\[
KE = \frac{1}{2} \times 25 \times 25
\]
\[
KE = 12.5 \times 25
\]
\[
KE = 312.5 \, \text{J}
\]

Answer: The object has kinetic energy, and \( KE = 312.5 \, \text{J} \).

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Final Answers:

1. Kinetic Energy: \( KE = 945 \, \text{J} \)
2. Gravitational Potential Energy: \( GPE \approx 251.7 \, \text{J} \)
3. Kinetic Energy: \( KE = 896,000 \, \text{J} \)
4. Gravitational Potential Energy: \( GPE \approx 1578.1 \, \text{J} \)
5. Gravitational Potential Energy: \( GPE \approx 8560.7 \, \text{J} \)
6. Gravitational Potential Energy: \( GPE \approx 69,500.7 \, \text{J} \)
7. Kinetic Energy: \( KE = 312.5 \, \text{J} \)

\boxed{\text{See detailed solutions above}}