Physics velocity question

Question

An incline plane has an angle of 56 degrees and a coefficient of kinetic friction of 0.25 with a 10-Kg mass sliding down the incline. The initial velocity down the plane is 5 m/s and the mass travels for a distance of 8 meters. There is also a constant 4-Newton force pushing it down the plane from some unknown source. What is the final velocity? Work this ONLY with conservation of energy.

Answer 1

On an energy basis, Work = Change in Kinetic Energy + Change in Potential Energy

Work is work from non-conservative forces, the 4 N down the ramp and the friction force up the ramp. Then do force *distance 4*8 - (.25)(10)(9.8)(.559) x 8

mgh2-mgh1 = 0 - 10*9.8*6.632 (Where 0 energy is defined at bottom of the ramp) 6.632 is height of ramp.

for kinetic energy, (.5)(10)(v2)^2 - (.5)(10)(5)^2 v2 = final velocity & 5 = initial velocity (given)

Collecting terms & solviing for v2, we find that the final velocity = 11.8 m/s