An object of mass 1 kg is falling from the heighth - 10 m. Calculate
(a) The total energy of an object at h = 10
(b) Potential energy of the object when it is at h = 4 m
(c) Kinetic energy of the object when it is at h = 4 m
(d) What will be the speed of the object when it hits the ground?
Assume `g = 10 ms^(-2))`

Explanation

(a) The gravitational force is a conservative force. So the total energy remains constant throughout the motion. At h = 10 m, the total energy E is entirely potential energy
`R=U=mgh=1xx10xx10=100J`
(b) The potential energy of the object at h = 4 m is
`U=-mgh=1xx10xx4=40J`
(c) Since the total energy is constant throughout the motion, the kinetic energy at h= 4m must be `KE=E- U=100-40=60j`
Alternatively, the kinetic energy could also be found from velocity of the object at 4 m. At the height 4 m, the object has fallen through a height of 6 m. The velocity after falling 6 m is calculated from the equation of motion,
`v=sqrt(2gh)=sqrt(2xx10xx6)=sqrt(120)ms^(-1)`
The kinetic energy is `KE=1/2mv^(2)=1/2xx1xx120=60j`
(d) When the object is just about to hit the ground, the total energy is completely kinetic and the potential energy, U= 0.
`E=KE=1/2mv^(2)=100J`
`v=sqrt(2/mKE)=sqrt(2/1xx100)=sqrt(200)=14.12ms^(-1)`