Question
1. give the difference between potential and kinetic energy. ii. Give two examples of each 2. An object of mass 0.6kg is thrown vertically up with a velocity of 25m/s. calculate the potential energy at the maximum height (Take g = 10m/s2) 3. Name and discuss the two types of potential energy. 4. when work is said to be done? 5. Mr. Brisbane stone weighting 5.0g falls from the top of a building, which is 15m high. calculate a. the potential energy of the stone at the start of fall b. the velocity half way through its fall and hence the kinetic energy at that point (Take g = 10m/s2)
Answers
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GPT-4o mini
Let's go through your questions one by one.
### 1. Difference between Potential and Kinetic Energy
- **Potential Energy (PE)**: This is the energy an object possesses due to its position or configuration. It is stored energy that has the potential to do work.
- **Kinetic Energy (KE)**: This is the energy an object possesses due to its motion. It is the energy of a moving object.
**Examples of Potential Energy**:
1. Gravitational Potential Energy of an object at a height (e.g., a rock held at a height above the ground).
2. Elastic Potential Energy in a compressed spring (e.g., a stretched rubber band).
**Examples of Kinetic Energy**:
1. A moving car (e.g., a car traveling at a speed of 60 km/h).
2. A baseball thrown into the air (e.g., a ball moving at 20 m/s).
### 2. Calculate the Potential Energy at Maximum Height
Given:
- Mass (m) = 0.6 kg
- Initial velocity (u) = 25 m/s
- Gravitational acceleration (g) = 10 m/s²
At maximum height, the kinetic energy is converted into potential energy. First, we need to find the maximum height reached.
The maximum height (h) can be found using the formula:
\[ v^2 = u^2 + 2gh \]
At maximum height, the final velocity (v) is 0:
\[ 0 = (25)^2 - 2 \cdot 10 \cdot h \]
\[ h = \frac{(25)^2}{2 \cdot 10} = \frac{625}{20} = 31.25 \, \text{m} \]
The potential energy (PE) at maximum height is calculated as:
\[ PE = mgh = 0.6 \times 10 \times 31.25 = 187.5 \, \text{J} \]
### 3. Two Types of Potential Energy
1. **Gravitational Potential Energy**:
- This is the potential energy associated with the gravitational force. It depends on the height of an object above a reference point and is given by the formula \( PE = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the height above the reference point.
2. **Elastic Potential Energy**:
- This energy is stored in elastic materials when they are stretched or compressed. It can be calculated using the formula \( PE = \frac{1}{2} k x^2 \), where \( k \) is the spring constant and \( x \) is the displacement of the spring from its equilibrium position.
### 4. When Work is Said to be Done?
Work is said to be done when a force acts on an object to cause displacement. This means that:
- The force must be applied,
- The object must be displaced in the direction of the applied force,
- The displacement must be greater than zero.
Mathematically, work (W) is defined as:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \( W \) is work,
- \( F \) is the force applied,
- \( d \) is the displacement of the object,
- \( \theta \) is the angle between the force and the direction of displacement.
### 5. Calculate Potential Energy and Velocity
**a. Calculate the Potential Energy of the Stone at the Start of Fall**
Given:
- Mass (m) = 5.0 g = 0.005 kg (convert grams to kilograms)
- Height (h) = 15 m
- Gravitational acceleration (g) = 10 m/s²
Potential Energy (PE) at the start:
\[ PE = mgh = 0.005 \times 10 \times 15 = 0.75 \, \text{J} \]
**b. Calculate the Velocity Halfway Through Its Fall and Kinetic Energy at That Point**
Height halfway (h) = 15 m / 2 = 7.5 m.
At this point, the potential energy is given by:
\[ PE_{halfway} = mgh_{halfway} = 0.005 \times 10 \times 7.5 = 0.375 \, \text{J} \]
The potential energy decreases as the stone falls, and all the lost potential energy converts into kinetic energy.
The total mechanical energy at the top is:
\[ \text{Total Energy} = PE_{initial} = 0.75 \, \text{J} \]
The kinetic energy (KE) halfway through the fall:
\[ KE_{halfway} = \text{Total Energy} - PE_{halfway} = 0.75 - 0.375 = 0.375 \, \text{J} \]
Now, to find the velocity (v) halfway through the fall, we can use the kinetic energy formula:
\[ KE = \frac{1}{2} mv^2 \]
\[ 0.375 = \frac{1}{2} \times 0.005 \times v^2 \]
\[ v^2 = \frac{0.375 \times 2}{0.005} = 150 \]
\[ v = \sqrt{150} \approx 12.25 \, \text{m/s} \]
### Summary of Answers
1. **Differences**: Detailed above.
2. **Potential Energy at Maximum Height**: 187.5 J.
3. **Types of PE**: Gravitational Potential Energy and Elastic Potential Energy.
4. **Work is Done**: When a force causes displacement.
5. **Potential Energy**: 0.75 J; **Kinetic Energy and Velocity halfway**: KE = 0.375 J, v ≈ 12.25 m/s.
### 1. Difference between Potential and Kinetic Energy
- **Potential Energy (PE)**: This is the energy an object possesses due to its position or configuration. It is stored energy that has the potential to do work.
- **Kinetic Energy (KE)**: This is the energy an object possesses due to its motion. It is the energy of a moving object.
**Examples of Potential Energy**:
1. Gravitational Potential Energy of an object at a height (e.g., a rock held at a height above the ground).
2. Elastic Potential Energy in a compressed spring (e.g., a stretched rubber band).
**Examples of Kinetic Energy**:
1. A moving car (e.g., a car traveling at a speed of 60 km/h).
2. A baseball thrown into the air (e.g., a ball moving at 20 m/s).
### 2. Calculate the Potential Energy at Maximum Height
Given:
- Mass (m) = 0.6 kg
- Initial velocity (u) = 25 m/s
- Gravitational acceleration (g) = 10 m/s²
At maximum height, the kinetic energy is converted into potential energy. First, we need to find the maximum height reached.
The maximum height (h) can be found using the formula:
\[ v^2 = u^2 + 2gh \]
At maximum height, the final velocity (v) is 0:
\[ 0 = (25)^2 - 2 \cdot 10 \cdot h \]
\[ h = \frac{(25)^2}{2 \cdot 10} = \frac{625}{20} = 31.25 \, \text{m} \]
The potential energy (PE) at maximum height is calculated as:
\[ PE = mgh = 0.6 \times 10 \times 31.25 = 187.5 \, \text{J} \]
### 3. Two Types of Potential Energy
1. **Gravitational Potential Energy**:
- This is the potential energy associated with the gravitational force. It depends on the height of an object above a reference point and is given by the formula \( PE = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the height above the reference point.
2. **Elastic Potential Energy**:
- This energy is stored in elastic materials when they are stretched or compressed. It can be calculated using the formula \( PE = \frac{1}{2} k x^2 \), where \( k \) is the spring constant and \( x \) is the displacement of the spring from its equilibrium position.
### 4. When Work is Said to be Done?
Work is said to be done when a force acts on an object to cause displacement. This means that:
- The force must be applied,
- The object must be displaced in the direction of the applied force,
- The displacement must be greater than zero.
Mathematically, work (W) is defined as:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \( W \) is work,
- \( F \) is the force applied,
- \( d \) is the displacement of the object,
- \( \theta \) is the angle between the force and the direction of displacement.
### 5. Calculate Potential Energy and Velocity
**a. Calculate the Potential Energy of the Stone at the Start of Fall**
Given:
- Mass (m) = 5.0 g = 0.005 kg (convert grams to kilograms)
- Height (h) = 15 m
- Gravitational acceleration (g) = 10 m/s²
Potential Energy (PE) at the start:
\[ PE = mgh = 0.005 \times 10 \times 15 = 0.75 \, \text{J} \]
**b. Calculate the Velocity Halfway Through Its Fall and Kinetic Energy at That Point**
Height halfway (h) = 15 m / 2 = 7.5 m.
At this point, the potential energy is given by:
\[ PE_{halfway} = mgh_{halfway} = 0.005 \times 10 \times 7.5 = 0.375 \, \text{J} \]
The potential energy decreases as the stone falls, and all the lost potential energy converts into kinetic energy.
The total mechanical energy at the top is:
\[ \text{Total Energy} = PE_{initial} = 0.75 \, \text{J} \]
The kinetic energy (KE) halfway through the fall:
\[ KE_{halfway} = \text{Total Energy} - PE_{halfway} = 0.75 - 0.375 = 0.375 \, \text{J} \]
Now, to find the velocity (v) halfway through the fall, we can use the kinetic energy formula:
\[ KE = \frac{1}{2} mv^2 \]
\[ 0.375 = \frac{1}{2} \times 0.005 \times v^2 \]
\[ v^2 = \frac{0.375 \times 2}{0.005} = 150 \]
\[ v = \sqrt{150} \approx 12.25 \, \text{m/s} \]
### Summary of Answers
1. **Differences**: Detailed above.
2. **Potential Energy at Maximum Height**: 187.5 J.
3. **Types of PE**: Gravitational Potential Energy and Elastic Potential Energy.
4. **Work is Done**: When a force causes displacement.
5. **Potential Energy**: 0.75 J; **Kinetic Energy and Velocity halfway**: KE = 0.375 J, v ≈ 12.25 m/s.