Question

a) A 24 Kg block is pushed against a vertical surface. The coefficient of friction between the surface and the block is 0.16. If the angle is 30^o, what is the minimum magnitude of P to hold the block still?

b) A 4 Kg block is placed at rest at a vertical height of 30 meters on a plane inclined at 4^o with the horizontal. If the surface is frictionless, how fast will the block be moving when it gets to the bottom of the plane?

Answer 1

a) from the free body diagram we have

P-Fn cos=0 ( horizontal direction)

so P=Fn*cos................1)

and in vertical direction
Fr-W=0

Fr=W

and we know that Fr( friction force)=Fncos30 and W=mg

now we have

Fncos30=Fg

Fn=Fg/ cos30=24kg*9.8m/s²/0.16*cos30=1697N

from eqn 1 we have

P=Fn*cos30=1697*cos30=1470N

so P=1470N

so the answer is 1470 N

b) from conservation of energy we have

P.E=K.E

mgh=1/2mv²

v=2gh....................1)

h=30*cos40=22.98m

so now using eqn 1

v=2*9.8*22.98=21.2 m/s

so the answer is 21m/s or 21.2m/s