Physics Question: Force, Power, and Incline

A 2402 kg block of granite is pulled up an incline that has an angle of inclination of 25.0 o with a constant speed of 1.10 m/s by a steam winch. The coefficient of kinetic friction between the block and the incline is 0.190. How much power must be supplied by the winch?

I have tried to separate answers to this and neither is correct. I find the tension in the rope pulling up the block by finding the normal force and multiplying it by the kinetic of friction, and then I multiply that by the velocity. What am I doing wrong? Thanks!

No, the Tension you worked out is not correct... you forgot the Block's weight sliding down the incline


Let's look at the resistive forces first (opposing the movement)

F// down the incline = mgsin(angle)
Ffric = u.Fn = umgcos(angle)

So the Tension and hence steam winch must apply this force to pull it up at a constant speed.

Fwinch = mgsin(angle) + umgcos(angle)
.... = mg[sin(angle) + ucos(angle)]

Now Power = Work / time
.. and work = Fd
Power = mg[sin(angle) + ucos(angle)] x 1.1 m / 1 second

Plug in the numbers - that should work

Component of weight down the plane=2402*9.8*sin25 N
Friction down the plane = 2402*9.8*cos25*0.19 N
Power= Work done per sec = 2402*9.8*(sin25+cos25*0.19)*1.1=15402 N.m/s (Watts)
or 15.402 KW