determine whether the objects in the following problems have kinetic or potential energy. then choose the correct formula to use. show all your work when solving.
ke =
pe=
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.

2. a baby carriage is sitting at the top of a hill that is 21 m high. the carriage has a mass of 10kg. the carriage has ____________ energy. calculate it.

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

4. what is the kinetic energy of a 3 - kilogram ball that is rolling at 2 meters per second?

5. what is the potential energy of a 3 kilogram - ball that is on the ground?

6. what is the kinetic energy of a 2,000 - kilogram boat moving at 5 m/sec?

7. what is the velocity of a 500 - kilogram elevator that has 4,000 joules of energy?

8. what is the mass of an object that creates 23,750 joules of energy by traveling at 35 m/sec?

b
the girl is swinging on the swing set. answer the questions below.
1. where is the girls pe changing to ke? ______b______
2. where does the girl have the most pe? ______c______
3. where does the girl have the most ke? ______b______
4. where is the girls ke changing to pe? ______b______

what is the law of conservation of energy?
how are potential and kinetic energy related to each other?

Question

determine whether the objects in the following problems have kinetic or potential energy. then choose the correct formula to use. show all your work when solving.
ke =
pe=
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.

2. a baby carriage is sitting at the top of a hill that is 21 m high. the carriage has a mass of 10kg. the carriage has ____________ energy. calculate it.

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

4. what is the kinetic energy of a 3 - kilogram ball that is rolling at 2 meters per second?

5. what is the potential energy of a 3 kilogram - ball that is on the ground?

6. what is the kinetic energy of a 2,000 - kilogram boat moving at 5 m/sec?

7. what is the velocity of a 500 - kilogram elevator that has 4,000 joules of energy?

8. what is the mass of an object that creates 23,750 joules of energy by traveling at 35 m/sec?

b
the girl is swinging on the swing set. answer the questions below.
1. where is the girls pe changing to ke? ______b______
2. where does the girl have the most pe? ______c______
3. where does the girl have the most ke? ______b______
4. where is the girls ke changing to pe? ______b______

what is the law of conservation of energy?
how are potential and kinetic energy related to each other?

Accepted Answer

### Problem 1:
# Explanation:
## Step1: Identify energy type (Kinetic, since moving)
Kinetic Energy formula: $ KE = \frac{1}{2}mv^2 $, where $ m = 2.1 \, \text{kg} $, $ v = 30 \, \text{m/s} $
## Step2: Substitute values into formula
$ KE = \frac{1}{2} \times 2.1 \times (30)^2 $
$ KE = 0.5 \times 2.1 \times 900 $
$ KE = 1.05 \times 900 = 945 \, \text{J} $
# Answer:
The ball has kinetic energy. Calculated value: $ 945 \, \text{J} $

### Problem 2:
# Explanation:
## Step1: Identify energy type (Potential, at height)
Potential Energy (Gravitational) formula: $ PE = mgh $, $ g = 9.8 \, \text{m/s}^2 $, $ m = 10 \, \text{kg} $, $ h = 21 \, \text{m} $
## Step2: Substitute values
$ PE = 10 \times 9.8 \times 21 $
$ PE = 98 \times 21 = 2058 \, \text{J} $
# Answer:
The carriage has potential energy. Calculated value: $ 2058 \, \text{J} $

### Problem 3:
# Explanation:
## Step1: Identify energy type (Kinetic, moving)
Use $ KE = \frac{1}{2}mv^2 $, $ m = 1720 \, \text{kg} $, $ v = 40 \, \text{m/s} $
## Step2: Calculate
$ KE = \frac{1}{2} \times 1720 \times (40)^2 $
$ KE = 860 \times 1600 = 1376000 \, \text{J} $
# Answer:
The car has kinetic energy. Calculated value: $ 1376000 \, \text{J} $

### Problem 4:
# Explanation:
## Step1: Use Kinetic Energy formula $ KE = \frac{1}{2}mv^2 $
$ m = 3 \, \text{kg} $, $ v = 2 \, \text{m/s} $
## Step2: Substitute
$ KE = \frac{1}{2} \times 3 \times (2)^2 = \frac{1}{2} \times 3 \times 4 = 6 \, \text{J} $
# Answer:
Kinetic energy is $ 6 \, \text{J} $

### Problem 5:
# Explanation:
Potential Energy (Gravitational) depends on height ($ PE = mgh $). If on the ground, $ h = 0 $. So $ PE = 3 \times 9.8 \times 0 = 0 \, \text{J} $
# Answer:
Potential energy is $ 0 \, \text{J} $ (since height is 0)

### Problem 6:
# Explanation:
## Step1: Use $ KE = \frac{1}{2}mv^2 $, $ m = 2000 \, \text{kg} $, $ v = 5 \, \text{m/s} $
## Step2: Calculate
$ KE = \frac{1}{2} \times 2000 \times (5)^2 = 1000 \times 25 = 25000 \, \text{J} $
# Answer:
Kinetic energy is $ 25000 \, \text{J} $

### Problem 7:
# Explanation:
## Step1: Given $ KE = 4000 \, \text{J} $, $ m = 500 \, \text{kg} $, use $ KE = \frac{1}{2}mv^2 $, solve for $ v $
## Step2: Rearrange formula: $ v = \sqrt{\frac{2KE}{m}} $
Substitute: $ v = \sqrt{\frac{2 \times 4000}{500}} = \sqrt{\frac{8000}{500}} = \sqrt{16} = 4 \, \text{m/s} $
# Answer:
Velocity is $ 4 \, \text{m/s} $

### Problem 8:
# Explanation:
## Step1: Given $ KE = 23750 \, \text{J} $, $ v = 30 \, \text{m/s} $, use $ KE = \frac{1}{2}mv^2 $, solve for $ m $
## Step2: Rearrange: $ m = \frac{2KE}{v^2} $
Substitute: $ m = \frac{2 \times 23750}{(30)^2} = \frac{47500}{900} \approx 52.78 \, \text{kg} $
# Answer:
Mass is approximately $ 52.78 \, \text{kg} $

### Part B (Swing Questions):
#### 1. Where is PE changing to KE?
# Brief Explanations:
As the girl moves from the highest point (A or C) to the lowest point (B), potential energy (due to height) decreases and kinetic energy (due to speed) increases. So between A/C to B (or during the downward swing towards B).
# Answer:
From the highest point (A or C) to the lowest point (B) (e.g., when moving from A to B or C to B)

#### 2. Where does the girl have the MOST PE?
# Brief Explanations:
Potential Energy depends on height ($ PE = mgh $). The highest points (A and C) have the maximum height, so maximum PE.
# Answer:
At the highest points (A and C)

#### 3. Where does the girl have the MOST KE?
# Brief Explanations:
Kinetic Energy depends on speed. At the lowest point (B), speed is maximum (since PE is converted to KE), so KE is maximum.
# Answer:
At the lowest point (B)

#### 4. Where is KE changing to PE?
# Brief Explanations:
As the girl moves from the lowest point (B) to the highest point (A or C), kinetic energy (due to speed) decreases and potential energy (due to height) increases. So between B to A/C (or during the upward swing from B to A or B to C).
# Answer:
From the lowest point (B) to the highest point (A or C) (e.g., when moving from B to A or B to C)

#### Law of Conservation of Energy:
# Brief Explanations:
Energy cannot be created or destroyed, only transferred or transformed from one form to another (e.g., PE ↔ KE in the swing). Total mechanical energy (PE + KE) remains constant (ignoring air resistance/friction).
# Answer:
Energy cannot be created or destroyed, only transferred/transformed between forms; total mechanical energy is conserved (in a closed system with no non - conservative forces).

#### How are PE and KE related?
# Brief Explanations:
In the swing, as the girl moves, PE and KE are interconverted. At highest points (A/C), PE is max, KE is min (speed ~0). At lowest point (B), KE is max, PE is min (height ~0). Total (PE + KE) remains constant (ideal case, no energy loss).
# Answer:
Potential and kinetic energy are interconverted: as height (PE) increases, speed (KE) decreases, and vice versa; their sum (total mechanical energy) is conserved (in an ideal system without energy loss).

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QUESTION IMAGE

Question

Explanation:

Problem 1:

Step1: Identify energy type (Kinetic, since moving)

Step2: Substitute values into formula

Step1: Identify energy type (Potential, at height)

Step2: Substitute values

Step1: Identify energy type (Kinetic, moving)

Step2: Calculate

Answer:

Problem 2: