Energy and work problem

Question

A 40 kg body starting from rest falls through a vertical distance of 0.25m to the ground, using energy methods,

a) determine its kinetic energy just before it hits the ground,

b) determine its velocity just before it hits the ground. 

Answer 1

The conservation of energy helps you in solving this exercise.

Step 1

Identify an initial position and write down the total energy given by the sum of the potential energy and the kinetic energy. In this case you have only potential energy since the exercise tells you that the body is at rest.

So the total energy, E_T= E_k +E_P =mgh

Step 2

Identify the final position and write down the total energy given by the sum of the potential energy and the kinetic energy. In this case you have only kinetic energy (just before hitting the ground the hight is h=0) since the exercise tells you that the body hits the ground.

So the total energy, E_T= E_k +E_P =1/2mv²

Step 3

These two quantities must be equal, hence mgh=1/2mv² or, gh=1/2v²

Given this, you have

a)The kinetic energy just before hitting the ground is given by the original potential energy equal to mgh=40*0.25*9.81 J = 98.1 J

b) from gh=1/2v² you can evaluate v=sqrt(2gh)=sqrt(2*9.81*0.25)=2.21 m/s

Best,

Davide