Kinetic Energy - Example 7.2-1

 

Consider a block being pushed along a smooth surface. The applied force P pushes the block causing the block to move, therefore, the force does work on the block.

 

 

What is the work done by force P if the block travels through a distance of Δx?

 

U = -PΔx
U = PΔx
U = 0

 

 

 

The work done by the force on the block gets converted to ....

 

Work
Kinetic energy
Potential energy

 

 

 

Using Newton’s second law (the equation of motion), determine the acceleration of the block.

 

a = mP
a = (P-mg)/m
a = P/m

 

 

 

Using the kinematic relationship ∫a dx = ∫v dv, determine the work done by force P on the block.

 

∫P dx = m∫v dv = m(v₂²-v₁²)/2
∫P dx = m∫v dv = mΔv
∫P dx = ∫v dv = Δv/2