To find the work done on the cart by the rope, we need to calculate the force exerted by the rope and then multiply it by the distance over which the force is applied.
First, let's find the force exerted by the rope. The force exerted by the rope can be divided into two components: a horizontal component and a vertical component.
The vertical component of the force is equal to the weight of the cart, which can be calculated as follows:
Weight = mass * gravity
Weight = 22.3 kg * 9.8 m/s^2
Weight = 218.54 N (Newtons)
The horizontal component of the force is equal to the force required to overcome the kinetic friction between the cart and the ground. This can be calculated as follows:
Frictional force = coefficient of kinetic friction * normal force
Normal force = mass * gravity * cos(theta)
Frictional force = 0.442 * (22.3 kg * 9.8 m/s^2 * cos(27.3 degrees))
Frictional force = 82.51 N
Now, let's find the force exerted by the rope:
Force by rope = sqrt(horizontal force^2 + vertical force^2)
Force by rope = sqrt((Frictional force)^2 + (Weight)^2)
Force by rope = sqrt((82.51 N)^2 + (218.54 N)^2)
Force by rope = 237.17 N
Finally, let's calculate the work done by the rope:
Work = force * distance
Work = 237.17 N * 9.3 m
Work = 2205.68 J
Therefore, the work done on the cart by the rope is 2205.68 Joules (J).