Thread: How much work is done on the cart by the rope?

A cart loaded with bricks has a total mass of 12.3 kg and is pulled at constant speed by a rope. The rope is inclined at 24.5 degrees above the horizontal and the cart moves 12.5 m on a horizontal surface. The coefficient of kinetic friction between ground and
cart is 0.503.

The acceleration of gravity is 9.8 m/ s^2 :

How much work is done on the cart by the rope? Answer in units of J.

Construct a free body diagram.

Let's solve without numbers first
N=Normal Force
T=Rope Tension
?=kinectic coeff.
?=angle with horizontal
m=mass
g=gravity acceleration
s=distance

x Forces: ?N-Tcos(?)=0 (I)
y Forces: Tsin(?)+N-mg (II)

First, solve for N by eliminating T by using (I) into (II)
we get
N=mg/(?tan(?)+1)

The force that does the work (recall F.s) is in the x direction

so, it is Tcos(?). but this is the same as ?N
s0 the work will be
W=mg?s/(?tan(?)+1)

plugging all the values in we get 616.6 J (it's all in MKS so units work)