Chapter 6: Problem 10
Assess Is it possible to do work on an object that remains at rest? Explain.
Short Answer
Expert verified
No, work requires displacement; an object at rest cannot have work done on it.
Step by step solution
01
Understanding Work
In physics, the concept of work is defined as the process of energy transfer to an object via the application of a force along a displacement. The formula for work is given by \( W = F \times d \times \cos(\theta) \), where \( W \) is the work done, \( F \) is the force applied, \( d \) is the displacement of the object, and \( \theta \) is the angle between the force and the displacement direction.
02
Analyzing the Displacement Component
For work to be done on an object, there must be a displacement. According to the formula \( W = F \times d \times \cos(\theta) \), if the displacement \( d = 0 \), then regardless of the force applied, the work done \( W \) will also be 0. This is because the displacement is a crucial component of the formula and determines the possibility of work being done.
03
Realizing the Implication
If an object remains at rest, it means there is no change in its position or no displacement \( d \). Hence, applying the formula for work, \( d \) becomes 0, leading to no work being done \( W = 0 \). This indicates it is not possible to do work on an object that remains at rest without displacement.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Energy Transfer
In physics, energy transfer is a fundamental concept that describes a change in energy from one form to another or from one object to another. This process is essential when we talk about doing work. Work is effectively a measure of energy transfer through the application of force over a distance.
When work is performed on an object, energy is transferred to that object, resulting in a change in its state – such as its speed or position.
When work is performed on an object, energy is transferred to that object, resulting in a change in its state – such as its speed or position.
- For example, lifting a book off the ground involves transferring energy from your muscles to the book.
- This energy goes into the book's increased gravitational potential as it rises.
Displacement
Displacement plays a crucial role in determining whether work is done. In physics, displacement refers to a change in the position of an object. It's important to distinguish displacement from distance; while distance is the total path length traveled, displacement is the shortest straight-line distance between starting and ending points, along with a direction.
- Work is only considered as being done when there is displacement.
- The formula for work, which includes displacement, is given by: \[ W = F \times d \times \cos(\theta) \] This formula indicates that if the displacement, \( d \), is zero, then the work, \( W \), is also zero.
Force Application
Force application is the act of applying a push or pull on an object. In terms of doing work, force is an essential component. The greater the force applied, the more potential work can be done, given that there is displacement involved.
Force is usually represented by the symbol \( F \) in physics equations.
Force is usually represented by the symbol \( F \) in physics equations.
- It's measured in newtons (N).
- The direction of force application also crucially affects how much work is done, which links into the angle of force.
Angle of Force
The angle of force is a critical concept that influences the amount of work done on an object. It refers to the angle between the direction of force applied and the direction of displacement. This angle affects the work done in a manner described by the cosine component in the work equation: \[ W = F \times d \times \cos(\theta) \]This formula indicates how the effective component of the force, in the direction of displacement, is calculated.
- If \( \theta = 0\), meaning the force is applied in the exact direction of displacement, full work is done as \( \cos(0) = 1\).
- If \( \theta = 90°\), meaning the force is applied perpendicular to the direction of displacement, no work is done since \( \cos(90°) = 0\).