Question

Assess Is it possible to do work on an object that remains at rest? Explain.

Short answer

No, work requires displacement; an object at rest cannot have work done on it.

Step-by-step solution

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.

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.

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.

Key concepts

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.

• 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.

The efficiency of energy transfer and how it is measured are key aspects of understanding work and mechanics in physics.

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.

For instance, if you push against a wall and it doesn't move, the displacement is zero, and thus no work is physically done on the wall even though force was applied.

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.

• 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.

Force by itself doesn't necessarily mean work is being done. This highlights that merely applying force on an object is not sufficient for work to occur unless part of that force causes actual motion or displacement.

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 \( \cos(90°) = 0\).

Understanding the angle of force helps in maximizing the efficiency of energy transfer through work.