Refer to the image below. M = 15 kg H = 26 m A student is looking to push a bloc

Question

Refer to the image below.

M = 15 kg

H = 26 m

A student is looking to push a block up a slide. The student needs to apply a force 'F' (in N) to the block of mass M kg for a distance 'H/2' meters from point A to B. When the student reaches point B he releases the block to slide through the rough patch and up the ramp. What force 'F2' is needed to push the box such that when released at point B it slides exactly halfway up the ramp to point C. (half the elevation of point D). What 'F2' is needed if you are to push with just enough force such that the block slides past the rough patch, up the ramp and while sliding down past the rough patch again comes to a complete stop at the end of the 1.0 m long patch?

Explanation / Answer

a)
net work done on the block , Wnet = work done by person - workdone by friction

Wnet = F1*H/2 - mue*M*g*x

Wnet = F1*13 - 0.35*15*9.8*1


M*g*H/2 = F1*13 - 0.35*13*9.8

15*9.8*13 = F1*13 - 31.85

F1 = (15*9.8*13 + 31.85)/13

= 149.45 N


b)
Workdone by person = workdone by friction

F2*H/2 = 2*mue*M*g*x

F2 = 4*mue*M*g*x/H

= 4*0.35*15*9.8*1/26

= 7.915 N

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