Answer:
W_b = 290.6 J
Explanation:
Given:-
- The initial velocity vi = 1.40 m/s
- The final velocity vf = 6.30 m/s
- The Length of the slope, L = 12.4 m
- The height of the slope, h = 2.35 m
- The frictional force, Ff = 41.0 N.
- The mass of the boy , m = 52.0 kg.
Find:-
Find the work he did in pushing forward on his wheels during the downhill ride.
Solution:-
- The work done by the boy on the wheels during his journey down the hill can be modeled by the work-energy principle. Where, the net work done W_net is equal to change in total mechanical energy of the system. We have:
Δ K.E + ΔP.E = W_net
Where,
ΔK.E : Change in kinetic Energy of the system
ΔP.E : Change in potential energy of the system.
- The net work done on the system consists off the work done the boy (W_b) and the work done by the system against resistive forces (W_f).
W_net = W_b - W_f
W_net = W_b - Ff * L
- The change in kinetic and potential energies can be expressed as:
0.5*m*( vf^2 - vi^2) - m*g*h = W_b - Ff * L
0.5*(52.0)*(6.3^2 - 1.40^2) - (52)(9.81)(2.35) = W_b -41 *12.4
-217.802 + 508.4 = W_b
W_b = 290.6 J