Pendulum Physics

Question

assuming the weight part of the pendulum has potential energy at the top and kinetic at the bottom

a teacher with a mass of 90kg is swinging, he's acting as a pendulum, he is 2.5meters up

a) what is the potential energy of the pendulum at the top of its swing 

b ) what is the kinetic energy of the pendulum at the top of it's swing

c) what is the potential energy of the pendulum at the bottom of its swing

d) what is the velocity of the pendulum at the bottom of its swing

you don t have to solve all of these, but please do some and explain how to do it.

Answer 1

You can answer to all those questions by considering the principle of energy conservation.

The sum of the kinetic energy (E_k) and the potential energy (E_p) is constant.

The potential energy of an object with mass m located at heigh h from the ground (which is arbitrary) is given by

E_p = mhg

In your case, the potential energy of the object with mass m=90 kg at height h=2.5 m is equal to mgh=2207.25 N. Therefore,

a) E_p = 2207.25 N

b)Ek =0 since the mass is still at the maximum height (v=0, and hence E_k =(1/2)mv² =0)

c) At the bottom of the swing, the potential energy is converted into kinetic energy, hence at the bottom you have E_k =2207.25 N (ignoring dissipative effects)

d) at the bottom of the swing you have E_k =2207.25=(1/2)mv² from which you can obtain v² =2*2207.25/90 = 49.05 m^2/s^2 and hence, v≈7 m/s e

Best,

Davide