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Chapter 7: Problem 1

Work How do you know when work is done by a force?

Short Answer

Expert verified
Work is done by a force when it causes displacement of an object. It's measured by the component of the force in the direction of the displacement multiplied by the magnitude of this displacement. If there's no displacement or the force applied is perpendicular to the direction of the movement, no work is done.

Step by step solution

01

Identify the Force

First, determine whether a force was applied to an object. If no force was applied, no work was done.
02

Identify Object Displacement

Look for any displacement, or movement, of the object. If there is no displacement, then no work was done, regardless of the force applied.
03

Determine the Direction of the Force and Displacement

Next, check the direction of both force and displacement. Part of the force may be in the same direction as the displacement.
04

Calculate the Work

If force was applied and displacement occurred, calculate the work done using the formula \( W = F \cdot d \cdot \cos(\theta) \), where \( W \) is work done, \( F \) is the force applied, \( d \) is the displacement, and \( \theta \) is the angle between the direction of force and displacement.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Force and Displacement
When we talk about force and displacement, we refer to two fundamental concepts in physics that are closely linked to the idea of work. Force is a push or pull upon an object resulting from its interaction with another object, and displacement is the object's overall movement from one position to another.

For work to be done in a physical sense, these two components must be present: an applied force and a displacement of the object due to that force. It's essential to understand that if an object is pushed or pulled (force) and it moves (displacement), then and only then, we can say that work has been performed on the object. The direction of displacement is crucial, as it must have a component along the direction of the applied force for work to be done. For example, if you push a wall and it doesn't move, there is a force but no displacement, therefore no work is done.
Calculating Work in Physics
If we want to calculate the work done by a force in physics, we use a simple yet powerful formula:
\[ W = F \cdot d \cdot \cos(\theta) \] where:
  • \( W \) is the work done on an object (measured in Joules in the SI system),
  • \( F \) represents the magnitude of the force applied (in Newtons),
  • \( d \) signifies the magnitude of the displacement (in meters), and
  • \( \theta \) is the angle between the force and displacement vectors.

It's essential to comprehend that work is only being done by the component of the force that acts in the direction of the displacement. If a force is applied in a direction perpendicular to displacement, no work is done in the classical physics sense because the force doesn't contribute to moving the object further.
Angle of Force and Displacement
The angle \( \theta \) between the force applied and the displacement is a critical element in determining the amount of work done. This angle directly influences the calculation since the work is the component of the force in the direction of displacement multiplied by the displacement's size.

When the force is applied in the same direction as the displacement (\( \theta = 0^\circ \)), the cosine of the angle is 1, leading to the maximum amount of work done for that force. This scenario is easy to visualize if you imagine pushing a box across a floor: when you push it directly (straight ahead), you apply the maximum force in that direction.

If the force is perpendicular to the displacement (\( \theta = 90^\circ \)), no work is done, because the cosine of \( 90^\circ \) is 0. This is like pushing against a wall 鈥� all your effort (force) does not result in any movement (displacement) of the wall. In real-life instances, the angle often falls between these two extremes, and the cosine function allows us to calculate the effective component of the force that is doing work.

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