A Roller Coaster With A Potential Energy Of $235,200 , J$ Sits At The Top Of A 30 M High Hill. What Is The Mass Of The Roller Coaster? (Formula: P E = M G H P E = Mgh PE = M G H )A. 800 Kg B. 7,840 Kg C. 8,000 Kg D. 78,400 Kg

Introduction

Potential energy is a fundamental concept in physics that describes the stored energy an object possesses due to its position or configuration. In this article, we will explore the relationship between potential energy, mass, and height, using the formula: $P E = mgh$. We will apply this formula to a real-world scenario, where a roller coaster with a known potential energy sits at the top of a 30 m high hill. Our goal is to determine the mass of the roller coaster.

The Formula: $P E = mgh$

The formula $P E = mgh$ describes the relationship between potential energy (PE), mass (m), and height (h). Here, g represents the acceleration due to gravity, which is approximately $9.8 \, m/s^2$ on Earth's surface. This formula is a fundamental concept in physics and is widely used to calculate potential energy in various scenarios.

Applying the Formula to the Roller Coaster

Let's apply the formula to the roller coaster scenario. We are given that the potential energy of the roller coaster is $235,200 \, J$ and the height of the hill is 30 m. We can use the formula to calculate the mass of the roller coaster:

$$P E = mgh$$

$$235,200 \, J = m \times 9.8 \, m/s^2 \times 30 \, m$$

To solve for mass (m), we can rearrange the formula:

$$m = \frac{P E}{g \times h}$$

$$m = \frac{235,200 \, J}{9.8 \, m/s^2 \times 30 \, m}$$

$$m = \frac{235,200 \, J}{294 \, m^2/s^2}$$

$$m = 800 \, kg$$

Conclusion

Using the formula $P E = mgh$, we have successfully calculated the mass of the roller coaster. The mass of the roller coaster is $800 \, kg$. This result is consistent with the given options, which include $800 \, kg$ as one of the possible answers.

Discussion

The calculation of mass using the formula $P E = mgh$ is a straightforward process. However, it is essential to ensure that the given values are accurate and that the formula is applied correctly. In this scenario, we assumed that the potential energy of the roller coaster is $235,200 \, J$ and the height of the hill is 30 m. If these values are incorrect, the calculated mass will also be incorrect.

Real-World Applications

The formula $P E = mgh$ has numerous real-world applications in various fields, including engineering, physics, and mathematics. It is used to calculate potential energy in various scenarios, such as:

• Calculating the potential energy of a roller coaster or a car at the top of a hill
• Determining the energy required to lift an object to a certain height
• Calculating the energy stored in a compressed spring or a stretched rubber band

Conclusion

In conclusion, the formula $P E = mgh$ is a fundamental concept in physics that describes the relationship between potential energy, mass, and height. By applying this formula to a real-world scenario, we have successfully calculated the mass of a roller coaster. This result highlights the importance of understanding and applying the formula in various scenarios.

References

• [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
• [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Options

A. 800 kg B. 7,840 kg C. 8,000 kg D. 78,400 kg

Answer

A. 800 kg