A 45.0-kg crate is dragged at constant velocity 8.20 m across a horizontal floor with a...

A 45.0-kg crate is dragged at constant velocity 8.20 m across a horizontal floor with a rope making a 30 degree angle above the horizontal. The coefficient of kinetic friction is 0.250. Find the work done by friction. Give your answer in Joules.

Expert Solution

as given the crate is dragged at constant velocity the net force acting on it is zero.
lets talk about the forces in horizontal plane first,
the horizontal component of the tension(T) in the rope(i.e.Tcos30) is equal to the frictional force which is acting in the opposite direction.
the tricky part here is to calculate the frictional force,it will not be simply calculated as (0.25)(45)(9.8),,
because there is a vertical component of the tension(Tsin30) in the rope which is reducing the effective weight of the crate,which is (45*9.8)-Tsin30.
Thus,the force of friction=(0.25)[(45*9.8)-Tsin30]
this is equated against the horizontal component of the tension in the rope(i.e.Tcos30).
we get,Tcos30=(0.25)[(45*9.8)-Tsin30]
Tcos30=(0.25)[441-T/2]
on solving you get T=111.3N.
the work done by rope is force*displacement*cos30
=111.3*(8.2)*(cos30)
=790joules.

the work done by friction is frictional force*displacement*cos180(since the direction of force is opposite to the direction of displacement)
as already stated the frictional force is equal to the horizontal component of tension(Tcos30),the answer becomes

=111.3(cos30)*(8.2)*cos180 (cos180=-1) = -790joules
the work done is in negative since the direction of force is opposite to the direction of displacement.

45.0-kg crate is dragged at constant velocity 8.20 m across a horizontal floor with a rope making a 30 degree angle above the horizontal. The coefficient of kinetic friction is 0.250

work done by friction = Ffr x d =

-?(9.81)45 x 8.2 = -904.9725 Joules

work done by rope = F?? x 8.2

F?? = Ffr ------------------------> [since the object is at constant velocity , a = 0 => F(resultant) = 0]

= (0.25)45(9.81) = 110.3625 N

=> work done by rope = 110.3625 x 8.2 = 904.9725 J

net work done = 904.9725 - 904.9725 = 0

genius_generous answered 2 years ago

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