Chapter 6: Problem 30
Is the change in potential energy when a box is lifted 1 meter off the ground the same on Earth and the Moon? Explain.
Short Answer
Expert verified
The change in potential energy is greater on Earth than on the Moon because Earth's gravity is stronger.
Step by step solution
01
Understand the Concept of Potential Energy
Potential energy due to gravity is the energy an object possesses because of its position in a gravitational field, usually relative to another object or the ground. It is given by the formula \( PE = mgh \), where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity, and \( h \) is the height above the reference point.
02
Compare Gravitational Acceleration on Earth and the Moon
Gravitational acceleration \( g \) varies between the Earth and the Moon. On Earth, \( g \approx 9.8 \, \text{m/s}^2 \), while on the Moon, \( g \approx 1.6 \, \text{m/s}^2 \). This difference affects the potential energy calculated for the same height.
03
Calculate Change in Potential Energy on Earth
Let's say the mass \( m \) of the box is \( m \). The change in potential energy when the box is lifted 1 meter on Earth is \( \Delta PE_{\text{Earth}} = m \cdot 9.8 \, \text{m/s}^2 \cdot 1 \, \text{m} \), which simplifies to \( \Delta PE_{\text{Earth}} = 9.8m \, \text{J} \).
04
Calculate Change in Potential Energy on the Moon
Similarly, lifting the same box 1 meter on the Moon results in \( \Delta PE_{\text{Moon}} = m \cdot 1.6 \, \text{m/s}^2 \cdot 1 \, \text{m} \), which simplifies to \( \Delta PE_{\text{Moon}} = 1.6m \, \text{J} \).
05
Compare Potential Energy Changes
From the calculations, \( \Delta PE_{\text{Earth}} = 9.8m \) and \( \Delta PE_{\text{Moon}} = 1.6m \). Clearly, \( \Delta PE_{\text{Earth}} > \Delta PE_{\text{Moon}} \). Thus, lifting the box 1 meter changes its potential energy more on Earth than on the Moon.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Gravitational Acceleration
Gravitational acceleration is a fundamental concept in physics that describes the force of gravity acting on objects due to their mass. This force causes objects to accelerate towards the center of a massive body, like Earth or the Moon.
- On Earth, the gravitational acceleration is approximately 9.8 meters per second squared (m/s2).
- On the Moon, the gravitational acceleration is much lower, about 1.6 m/s2.
Energy in Gravitational Fields
Energy in gravitational fields is primarily expressed as potential energy, which depends on an object's position within a gravitational field. This energy is often referred to as gravitational potential energy and is a central concept in understanding how objects interact with gravitational forces.
The formula for gravitational potential energy is:\[ PE = mgh \]where:
For instance, lifting an object higher in the field increases its potential energy due to the increased height \( h \). Moreover, the same mass will have different potential energy on Earth compared to the Moon, predominantly because of the difference in \( g \). Thus, understanding energy in gravitational fields helps explain the effects of gravity on objects in various environments.
The formula for gravitational potential energy is:\[ PE = mgh \]where:
- \( m \) is the mass of the object,
- \( g \) is the gravitational acceleration, and
- \( h \) is the height above the reference point (usually the ground).
For instance, lifting an object higher in the field increases its potential energy due to the increased height \( h \). Moreover, the same mass will have different potential energy on Earth compared to the Moon, predominantly because of the difference in \( g \). Thus, understanding energy in gravitational fields helps explain the effects of gravity on objects in various environments.
Physics Education
Physics education provides a foundation for comprehending how the universe operates, from the smallest particles to the largest systems. One major objective of physics education is to help students grasp core principles like gravitational acceleration and energy in gravitational fields.
Using practical examples such as calculating potential energy can significantly enhance understanding and interest in physics.
By actively solving related problems, students learn:
By actively solving related problems, students learn:
- To apply mathematical formulas in real-world scenarios,
- Understand the implications of changing variables,
- Compare and contrast outcomes in different physical environments.