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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.
These values are different because the Earth's mass is greater than the Moon's, resulting in a stronger gravitational pull. Consequently, the same object will weigh less on the Moon than it does on Earth. This variation in gravitational acceleration directly impacts potential energy, as seen in the calculations for lifting a box. When determining potential energy in physics problems, it is crucial to know the specific gravitational acceleration where the problem takes place.
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:
  • \( m \) is the mass of the object,
  • \( g \) is the gravitational acceleration, and
  • \( h \) is the height above the reference point (usually the ground).
When you alter any of these three variables, you will change the potential energy.
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:
  • To apply mathematical formulas in real-world scenarios,
  • Understand the implications of changing variables,
  • Compare and contrast outcomes in different physical environments.
Engaging with these concepts not only builds scientific literacy but also fosters critical thinking and problem-solving skills. Thus, making physics education a valuable part of learning that influences everyday decisions and broadens one's curiosity about natural phenomena.

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Most popular questions from this chapter

You pick up a 3.4-kg can of paint from the ground and lift it to a height of \(1.8 \mathrm{~m}\). (a) How much work do you do on the can of paint? (b) You hold the can stationary for half a minute, waiting for a friend on a ladder to take it. How much work do you do during this time? (c) Your friend decides not to use the paint, so you lower it back to the ground. How much work do you do on the can as you lower it?

Predict \& Explain Ball 1 is dropped to the ground from rest. Ball 2 is thrown to the ground with an initial downward speed. Assuming that the balls have the same mass and are released from the same height, is the change in gravitational potential energy of ball 1 greater than, less than, or equal to the change in gravitational potential energy of ball 2? (b) Choose the best explanation from among the following: A. Ball 2 has the greater total energy, and therefore more of its energy can go into gravitational potential energy. b. The gravitational potential energy depends only on the mass of the ball and its initial height above the ground. C. All of the initial energy of ball 1 is gravitational potential energy.

An object has a speed of \(3.5 \mathrm{~m} / \mathrm{s}\) and a kinetic energy of \(14 \mathrm{~J}\) at \(t=0\). At \(t=5.0 \mathrm{~s}\) the object has a speed of \(4.7 \mathrm{~m} / \mathrm{s}\). (a) What is the mass of the object? (b) What is the kinetic energy of the object at \(t=5.0 \mathrm{~s}\) ? (c) How much work was done on the object between \(t=0\) and \(t=5.0 \mathrm{~s}\) ?

Rank Four joggers have the following masses and speeds: \begin{tabular}{|c|c|c|} \hline Jogger & Mass & Speed \\ \hline A & \(m\) & \(v\) \\ \hline B & \(m / 2\) & \(3 v\) \\ \hline C & \(3 m\) & \(v / 2\) \\ \hline D & \(4 m\) & \(v / 2\) \\ \hline \end{tabular} Rank the joggers in order of increasing kinetic energy. Indicate ties where appropriate.

A 5.76-kg rock is dropped and allowed to fall freely. Find the initial kinetic energy, the final kinetic energy, and the change in kinetic energy for (a) the first \(2.00 \mathrm{~m}\) of fall and (b) the second \(2.00 \mathrm{~m}\) of fall.

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