Work Done by a Variable Force - Problem L1



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.


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?

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


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

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?
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


Application of work-energy theorem in problems involving gravity

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.
Change in kinetic energy is
Using work-energy theorem, work done is given by,


Application of work-energy theorem in problems involving springs

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 = .
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.