Mechanics - work, energy and power

Question

A stone of mass 50kg starts from rest and is dragged 35m up a slope inclined at 7 degrees to the horizontal by a rope inclined at 25 degrees to the slope. the tension in the rope is 120N and the resistance to motion of the stone is 20N. calculate the speed of the stone after it has moved 35m up the slope.

Any help would be appreciated, as I'm not sure whether there is a easy way to approach this question as all the methods I've tried lead to the dead ends.

Answer 1

HINT

Let use that

• net force $F=120 \sin 25° - mg\sin 7° - 20$
• acceleration $a=\frac F m$ with $m=50 kg$
• distance $s=\frac12 a t^2=35$ to find $t$
• $v=at$ to find $v$

Answer 2

you could use the Work-Energy Principle. The work done by the external forces (the tension and the resistance) is $$120\cos25\times 35-20\times35$$

This is equal to the increase in mechanical energy (KE and GPE) which is $$\frac 1250v^2+50g\times 35\sin7$$

from which you can get $v$