# Work Done by a Variable Force - Problem L1

Physics

## example

### Friction and Spring Force acting on a body

Question: A kg body is dropped from height of m onto a spring of spring constant N/m as shown in the figure. A frictional force equivalent to kgwt acts on the body. What will be the speed of the body just before striking the spring? (Take )

Solution: We know that the change of kinetic energy is equal to work done by the system.
Change of Kinetic energy
Work done , where , friction force.
Now,

## example

### Use of Work Energy Theorem in Body Under Frictional Force

Example:  A kg block slides on a horizontal floor with a speed of m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is N and spring constant is N/m. What is the spring compression?

Solution:
The total kinetic energy possessed by the block goes into the potential energy of the spring and the work done against friction.Let be the compression of the spring.Thus

## example

### Application of work-energy theorem for a body under constant external force

Example:
A gm ball moving at m/s slows down uniformly until it stops. If the ball travels m, what was the average net force applied while it was coming to a stop?
Solution:
Initial kinetic energy,
Final kinetic energy,
Change in kinetic energy,
By work energy theorem, work done equals change in kinetic energy.

For a constant force, work done is

## example

### Application of work-energy theorem in problems involving gravity

Example:
A particle of mass g is thrown vertically upwards with a speed of m/s. Find the work done by the force of gravity during the time the particle goes up.
Solution:
Change in kinetic energy is
Using work-energy theorem, work done is given by,

## example

### Application of work-energy theorem in problems involving springs

Example:
A body of mass kg is connected to a spring. Under influence of a constant external force, maximum elongation in the spring is m. Now the external force is removed, find the maximum speed of the mass. Given spring constant = .
Solution:
Spring force on the body is given by,
Work done by spring force is given by,

By work-energy theorem, this equals the change in kinetic energy.

For maximum speed, is maximum, i.e.

## Work Done by a Variable Force

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