## Work Energy Theorem for a Variable Force – Class 11 | Chapter – 6 | Physics Short Notes Series PDF for NEET & JEE

Work Energy Theorem: The work-energy theorem is a fundamental concept in physics that relates the work done on an object to its change in kinetic energy. It states that the net work done on an object is equal to the change in its kinetic energy. The work energy theorem is a powerful tool for understanding the relationship between work and energy in physical systems. It allows us to predict the motion of objects based on the work done on them and the resulting changes in their kinetic energy.

## Work Energy Theorem

1. The work energy theorem states that the net work done on an object is equal to the change in its kinetic energy. That is:

Wnet = ΔKE

Where,

• Wnet is the net work done on the object.
• ΔKE is the change in the object’s kinetic energy.

2. When the force acting on an object is constant, the work done by the force can be calculated as:

W = F × d × cos(θ)

Where,

• F is the magnitude of the force,
• d is the distance moved by the object, and
• θ is the angle between the force and the displacement

However, when the force acting on an object is variable, the work done by the force can be calculated by dividing the displacement into small intervals and calculating the work done by each interval. This is known as integration.

3. The work done by a variable force over a distance d is given by the following equation:

W = ∫ F(x) dx

Where,

• F(x) is the force as a function of the position x along the path of the object.

Using the work-energy theorem, we can relate the work done by a variable force to the change in kinetic energy of the object:

∫ F(x) dx = ΔKE

This equation can be used to solve problems involving variable forces, by integrating the force over the distance and equating it to the change in kinetic energy of the object.

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