Answer:
To calculate the total energy of the ball after falling a distance of 40m, we can use the conservation of mechanical energy, which states that the total mechanical energy of the system remains constant in the absence of non-conservative forces like air resistance.
Explanation:
he total mechanical energy (E) of the ball consists of its potential energy (PE) at the initial height and its kinetic energy (KE) at any given height.Given:Mass of the ball (m) = 8 kgInitial height (h_initial) = 100 mFinal height (h_final) = 40 mGravitational acceleration (g) = 9.81 m/s²Calculate the initial potential energy (PE_initial): [ PE_{initial} = mgh_{initial} ] [ PE_{initial} = (8 , \text{kg})(9.81 , \text{m/s}^2)(100 , \text{m}) ] [ PE_{initial} = 7848 , \text{J} ]Calculate the final potential energy (PE_final) at a height of 40m: [ PE_{final} = mgh_{final} ] [ PE_{final} = (8 , \text{kg})(9.81 , \text{m/s}^2)(40 , \text{m}) ] [ PE_{final} = 3139.2 , \text{J} ]Calculate the kinetic energy (KE_final) at a height of 40m: Since the ball falls from rest, all the initial potential energy will be converted into kinetic energy at the final height. [ KE_{final} = PE_{initial} - PE_{final} ] [ KE_{final} = 7848 , \text{J} - 3139.2 , \text{J} ] [ KE_{final} = 4708.8 , \text{J} ]Therefore, the total energy of the ball after falling a distance of 40m is ( KE_{final} = 4708.8 , \text{J} ).
