Question

A mass m slides down a smooth inclined plane from an ini tial vertical height h, making an angle with the horizontal. (a) the work done by a force is the sum of the work done by the components of the force

Answer 1

i’ll use m for mass, h for height, • for theta, u for mu, and W for work.

we see that m slides down at a constant acceleration.

we summate our forces in the x-direction upon reorienting our axis, so:
Fnet=ma
Fxgravity-Ffriction=ma
mgsin•-umg=ma
gsin•-ug=a

this is our summation of forces, therefore the work done by any of the forces is any of these components taken out of the summation. example of work due to friction:
W=Fd
W=Ffriction(d)
W=-umgd