Answer :
- Identify the given values: mass $m = 25$ kg, height $h = 3$ m, and gravity $g = 9.8$ m/s$^2$.
- Apply the potential energy formula: $PE = mgh$.
- Substitute the values into the formula: $PE = 25 \times 9.8 \times 3$.
- Calculate the potential energy: $PE = 735$ J. The final answer is $\boxed{735 \text{ J}}$.
### Explanation
1. Understanding the Problem
We are given the mass of the bicycle (m = 25 kg), the height of the hill (h = 3 m), and the formula for potential energy (PE = mgh). We also know that the acceleration due to gravity (g) is approximately 9.8 m/s². Our goal is to calculate the potential energy of the bicycle at the top of the hill.
2. Applying the Formula
Now, we will use the formula for potential energy: $PE = mgh$. We substitute the given values into the formula: $PE = 25 \text{ kg} \times 9.8 \text{ m/s}^2 \times 3 \text{ m}$.
3. Calculating Potential Energy
Calculating the potential energy: $PE = 25 \times 9.8 \times 3 = 735$. Therefore, the potential energy of the bicycle is 735 Joules.
4. Final Answer
The potential energy of the 25 kg bicycle at the top of a 3 m high hill is 735 J.
### Examples
Potential energy is a crucial concept in physics and has many real-world applications. For example, when designing roller coasters, engineers use the principle of potential energy to determine the height of the initial hill. The potential energy at the top of the hill is converted into kinetic energy as the coaster descends, providing the necessary speed and momentum for the rest of the ride. Understanding and calculating potential energy helps ensure the roller coaster has enough energy to complete the track safely and excitingly. Similarly, in hydroelectric power plants, the potential energy of water stored at a height is converted into electrical energy.
- Apply the potential energy formula: $PE = mgh$.
- Substitute the values into the formula: $PE = 25 \times 9.8 \times 3$.
- Calculate the potential energy: $PE = 735$ J. The final answer is $\boxed{735 \text{ J}}$.
### Explanation
1. Understanding the Problem
We are given the mass of the bicycle (m = 25 kg), the height of the hill (h = 3 m), and the formula for potential energy (PE = mgh). We also know that the acceleration due to gravity (g) is approximately 9.8 m/s². Our goal is to calculate the potential energy of the bicycle at the top of the hill.
2. Applying the Formula
Now, we will use the formula for potential energy: $PE = mgh$. We substitute the given values into the formula: $PE = 25 \text{ kg} \times 9.8 \text{ m/s}^2 \times 3 \text{ m}$.
3. Calculating Potential Energy
Calculating the potential energy: $PE = 25 \times 9.8 \times 3 = 735$. Therefore, the potential energy of the bicycle is 735 Joules.
4. Final Answer
The potential energy of the 25 kg bicycle at the top of a 3 m high hill is 735 J.
### Examples
Potential energy is a crucial concept in physics and has many real-world applications. For example, when designing roller coasters, engineers use the principle of potential energy to determine the height of the initial hill. The potential energy at the top of the hill is converted into kinetic energy as the coaster descends, providing the necessary speed and momentum for the rest of the ride. Understanding and calculating potential energy helps ensure the roller coaster has enough energy to complete the track safely and excitingly. Similarly, in hydroelectric power plants, the potential energy of water stored at a height is converted into electrical energy.
