Kinetic and Potential Energy Worksheet with questions and calculations.

Problem Analysis:

The task involves classifying examples into kinetic energy (KE) and potential energy (PE), as well as solving problems using the formulas for kinetic and potential energy. Let's break it down step by step.

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Part 1: Classify the Following as a Type of Potential Energy or Kinetic Energy

We are given 10 scenarios, and we need to classify them into kinetic energy (KE) or potential energy (PE).

#### Definitions:
- Kinetic Energy (KE): Energy due to motion.
- Potential Energy (PE): Stored energy due to position or configuration.

#### Scenarios:
1. A bicyclist pedaling up a hill.
- Explanation: The bicyclist is moving, so this is kinetic energy.
- Classification: KE

2. An author with his book.
- Explanation: The book is stationary, so there is no motion. However, if the author lifts the book, it could have gravitational potential energy.
- Classification: PE (assuming the book is lifted)

3. A volleyball player spiking a ball.
- Explanation: The ball is in motion during the spike.
- Classification: KE

4. A football thrown to someone.
- Explanation: The football is in motion after being thrown.
- Classification: KE

5. The chemical bonds in sugar.
- Explanation: Chemical bonds store energy, which is a form of potential energy.
- Classification: PE

6. The wind blowing through your hair.
- Explanation: The wind is moving air, so this is kinetic energy.
- Classification: KE

7. Walking down the street.
- Explanation: You are in motion while walking.
- Classification: KE

8. Sitting at the top of a tree.
- Explanation: Sitting at the top of a tree means you have gravitational potential energy due to height.
- Classification: PE

9. A bowling ball rolling down the alley.
- Explanation: The bowling ball is in motion.
- Classification: KE

10. A bowling ball sitting on the rack.
- Explanation: The bowling ball is stationary, so it has no kinetic energy. However, if it is elevated, it has gravitational potential energy.
- Classification: PE

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Part 2: Examples of Kinetic and Potential Energy

We are asked to find two examples of kinetic energy and two examples of potential energy from our home.

#### Examples:
1. Kinetic Energy (KE):
- A fan spinning in the room.
- A toy car rolling down a ramp.

2. Potential Energy (PE):
- A book placed on a high shelf.
- A stretched rubber band ready to be released.

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Part 3: Understanding Kinetic Energy

We are asked to identify what kinetic energy depends on.

#### Formula for Kinetic Energy:
$$
KE = \frac{1}{2}mv^2
$$
Where:
- \( m \) is the mass of the object.
- \( v \) is the velocity of the object.

#### Answer:
- Kinetic energy depends on both mass and velocity.

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Part 4: Solve Problems Using Formulas

#### Problem 15: Baby Carriage Climbing a Hill
A baby carriage is sitting at the top of a hill that is 2 m high. The carriage with the baby has a mass of 3.5 kg. Calculate its potential energy.

#### Formula for Gravitational Potential Energy:
$$
PE = mgh
$$
Where:
- \( m \) is the mass (3.5 kg).
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).
- \( h \) is the height (2 m).

#### Calculation:
$$
PE = (3.5 \, \text{kg}) \times (9.8 \, \text{m/s}^2) \times (2 \, \text{m})
$$
$$
PE = 3.5 \times 9.8 \times 2
$$
$$
PE = 68.6 \, \text{J}
$$

#### Answer:
$$
\boxed{68.6 \, \text{J}}
$$

#### Problem 17: Car Traveling with Velocity
A car is traveling with a velocity of 60 km/h and has a mass of 1320 kg. The car has _______ kinetic energy. Calculate it.

#### Step 1: Convert Velocity to m/s
$$
60 \, \text{km/h} = 60 \times \frac{1000 \, \text{m}}{3600 \, \text{s}} = 16.67 \, \text{m/s}
$$

#### Step 2: Use the Kinetic Energy Formula
$$
KE = \frac{1}{2}mv^2
$$
Where:
- \( m = 1320 \, \text{kg} \)
- \( v = 16.67 \, \text{m/s} \)

#### Calculation:
$$
KE = \frac{1}{2} \times 1320 \times (16.67)^2
$$
$$
KE = 660 \times 277.89
$$
$$
KE = 183,725.4 \, \text{J}
$$

#### Answer:
$$
\boxed{183,725.4 \, \text{J}}
$$

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Final Answers:

1. Classification:
- KE: 1, 3, 4, 6, 7, 9
- PE: 2, 5, 8, 10

2. Examples:
- KE: Fan spinning, toy car rolling.
- PE: Book on a shelf, stretched rubber band.

3. Kinetic Energy Depends On: Mass and Velocity.

4. Calculations:
- Problem 15: \( \boxed{68.6 \, \text{J}} \)
- Problem 17: \( \boxed{183,725.4 \, \text{J}} \)