NEED Help BAD!! 45 kg trunk is pushed 5.2 m at constant speed up a 30° incline?

Question

A 45 kg trunk is pushed 5.2 m at constant speed up a 30° incline by a constant horizontal force. The coefficient of kinetic friction between the trunk and the incline is 0.24.

Calculate the work done by the applied horizontal force.

Calculate the work done by the weight of the trunk.

How much energy was dissipated by the frictional force acting on the trunk?

Now suppose the 45 kg trunk is pushed 5.2 m at constant speed up a 30° incline by a force along the plane (not as in the figure). The coefficient of kinetic friction between the trunk and the incline is 0.24.

Calculate the work done by the applied force.
Calculate the work done by the weight of the trunk.
How much energy was dissipated by the frictional force acting on the trunk?

Answer 1

Since the speed is constant and the force is constant, the work balances the increase in potential energy due to gravity and work done by friction

Since the force is horizontal it adds to the normal force of the trunk

N=m*g*cos(30)+sin(30)*F
so the friction is N*µ
and the work done by friction is N*µ*5.2

The parallel component of the force must balance the parallel component of the weight and friction

F*cos(30)=m*g*sin(30)+N*µ
F*cos(30)=m*g*sin(30)+
(m*g*cos(30)+sin(30)*F)µ

F*(cos(30)-sin(30)*µ)=
m*g*(sin(30)+cos(30)*µ)

F=m*g*(sin(30)+cos(30)*µ)/
(cos(30)-sin(30)*µ)

using g=9.81
F=m*g*(sin(30)+cos(30)*µ)/
(cos(30)-sin(30)*µ)

F=414 N

The work done by F is
=414*5.2*cos(30)
=1889 J

the work done by friction can be calculated two ways. I will do it both ways to check my work:

Using
N*µ*5.2
=(m*g*cos(30)+
sin(30)*F)*.24*5.2

=754 J

the work done by friction should equal the work done by F plus the gain in potential energy

1889=754+m*g*sin(30)*5.2
1901 which is less than 1% error


The work done by the weight of the trunk is
m*g*sin(30)*5.2

=1148



For part 2, the calculations are simplified
N=m*g*cos(30)
F=N*µ
F=m*g*(cos(30)*.24+sin(30)

F=314 N

The work done by the force is

=314*5.2
=1632 J

The work done by the frictional force is 484 J

The work done by the weight of the trunk is 1148 J

Note that the friction and weight works add to the work done by the force.

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