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Answer :
- Identify the given values: mass (m) = 25 kg, height (h) = 3 m, and acceleration due to gravity (g) = 9.8 m/s².
- Apply the formula for potential energy: $PE = mgh$.
- Substitute the values into the formula: $PE = 25 \times 9.8 \times 3$.
- Calculate the potential energy: $PE = 735 \text{ J}$. The final answer is $\boxed{735 \text{ J}}$.
### Explanation
1. Understanding the Problem
We are given a bicycle with a mass of 25 kg resting at the top of a hill that is 3 m high. We are asked to find the potential energy (PE) of the bicycle. The formula for potential energy is given as $PE = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height. We know that the standard value for $g$ is approximately 9.8 m/s².
2. Substituting the Values
Now, we will substitute the given values into the formula: $PE = mgh$. We have $m = 25 \text{ kg}$, $g = 9.8 \text{ m/s}^2$, and $h = 3 \text{ m}$. Therefore, $PE = 25 \times 9.8 \times 3$.
3. Calculating Potential Energy
Let's calculate the potential energy: $PE = 25 \times 9.8 \times 3 = 735$. The potential energy is 735 Joules.
4. Final Answer
Therefore, the potential energy of the bicycle is 735 J.
### Examples
Potential energy is a fundamental concept in physics that has many real-world applications. For example, when designing roller coasters, engineers use the concept of potential energy to determine the height of the initial hill needed to provide enough energy for the coaster to complete the ride. Similarly, in hydroelectric power plants, the potential energy of water stored at a height is converted into electrical energy. Understanding potential energy helps in designing efficient systems for energy generation and storage.
- Apply the formula for potential energy: $PE = mgh$.
- Substitute the values into the formula: $PE = 25 \times 9.8 \times 3$.
- Calculate the potential energy: $PE = 735 \text{ J}$. The final answer is $\boxed{735 \text{ J}}$.
### Explanation
1. Understanding the Problem
We are given a bicycle with a mass of 25 kg resting at the top of a hill that is 3 m high. We are asked to find the potential energy (PE) of the bicycle. The formula for potential energy is given as $PE = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height. We know that the standard value for $g$ is approximately 9.8 m/s².
2. Substituting the Values
Now, we will substitute the given values into the formula: $PE = mgh$. We have $m = 25 \text{ kg}$, $g = 9.8 \text{ m/s}^2$, and $h = 3 \text{ m}$. Therefore, $PE = 25 \times 9.8 \times 3$.
3. Calculating Potential Energy
Let's calculate the potential energy: $PE = 25 \times 9.8 \times 3 = 735$. The potential energy is 735 Joules.
4. Final Answer
Therefore, the potential energy of the bicycle is 735 J.
### Examples
Potential energy is a fundamental concept in physics that has many real-world applications. For example, when designing roller coasters, engineers use the concept of potential energy to determine the height of the initial hill needed to provide enough energy for the coaster to complete the ride. Similarly, in hydroelectric power plants, the potential energy of water stored at a height is converted into electrical energy. Understanding potential energy helps in designing efficient systems for energy generation and storage.
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