Mechanical a body of mass 50kg

Question

a body of mass 50kg is suspended at a height of 20m above the ground . Calculate 

a) the potential ener stored in the body at this height 

b) if the body is allowed to fall freely, the velocity when it is 10m above the ground

Answer 1

a) the potential energy, PE stored in the body at this height 

 

E = PE + KE

E = mgh + (1/2)mv²

 

PE = mgh

PE = (50kg)*(9.8ms^-2)*(20m)

PE = 9800 J

b) if the body is allowed to fall freely, the velocity when it is 10m above the ground

 

We know the total energy, E = 9800 J because KE was zero at the suspended height. (E = PE + 0) Use the total energy formula to solve for velocity at the new height 10m.

 

E = PE + KE

E = mgh + (1/2)mv²

 

9800 J = (50kg)*(-9.8ms^-2)*(10m) + (1/2)*(50kg)*v²

 

9800 J = -4900 J + 250mkg*v²

14700 J = 250mkg*v²

14700 j / 250mkg = v²

58.8 m²s^-2 = v²

Sqrt(58.8 m²s^-2) = v

 

7.67 ms^-1 = v