Question

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

Short answer

No, work requires displacement; a stationary object means no work is done.

Step-by-step solution

Understanding Work

To solve this problem, let's start by understanding what 'work' means in physics. Work is defined as the process of transferring energy to an object via the application of a force along a displacement. Mathematically, it's given by the equation: \( W = F imes d imes \cos(\theta) \), where \( F \) is the force applied, \( d \) is the displacement of the object, and \( \theta \) is the angle between the force and the displacement.

Analyzing the Condition of Rest

Next, we need to analyze the condition that the object remains at rest. If the object remains at rest, its displacement \( d = 0 \). Even if you apply a force \( F \), according to the work formula \( W = F imes d imes \cos(\theta) \), the work done is zero as long as \( d = 0 \).

Conclusion on Work and Rest

As per the formula, when the displacement \( d \) is zero, the work done on the object is zero regardless of the force applied or the angle. Hence, it is not possible to do work on an object if it remains at rest because work requires displacement.

Key concepts

Displacement in Physics

Displacement is a core concept in physics that helps us understand the movement of objects. It refers to how far an object moves in a straight line and in a specific direction. Unlike distance, which only measures how much ground an object covers, displacement considers both the magnitude and the direction of movement.
In the context of work, displacement is crucial because it's part of the equation that defines work:

• Work is only done when there is displacement.
• Even if a force is applied, no displacement means no work is done.
• Displacement is a vector quantity, which means it has both magnitude and direction.

This means if an object stays in the same place without moving, its displacement is zero. As a result, no work is accomplished even if a force is exerted. This helps explain why it's impossible to do work on an object that remains at rest.

Understanding Force

Force is any interaction that, when unopposed, changes the motion of an object. In simple terms, it's a push or a pull exerted on an object.
In physics, force is measured in newtons (N) and is often associated with causing objects to accelerate or change direction. Its role in the context of work is significant:

• Without force, there cannot be displacement or work.
• Force is crucial for energy transfer during work.
• The direction of force affects how much work is done.

The angle between the applied force and the direction of displacement affects how effectively the force contributes to work. When the force and displacement are in the same direction, the full magnitude of the force contributes to doing work. No work is done if there's no displacement, even with an applied force. This showcases why merely applying a force on a resting object does not result in work being done.

The Role of Energy Transfer

Energy transfer is central to understanding why work is done on an object. When work happens, there is a transfer of energy from one system to another.
Work and energy transfer are deeply intertwined in physics:

• Work is essentially the transfer of energy.
• When work is done, energy is transferred to or from an object.
• No energy transfer occurs if there is no displacement.

When you apply a force to an object and it moves (displacement occurs), energy from the force is transferred to the object, doing work. This energy might make the object move faster, gain height, or increase its potential or kinetic energy. If the object doesn't move, no energy is transferred, hence no work. This connection highlights the importance of displacement in determining whether energy transfer leads to work.