How much work is done by the boy pulling his sister d = 25.0 m in a wagon as shown in figure below? Assume no friction acts on the wagon and he pulls with a force of 65.0 N and at an angle θ = 31.0°.

To calculate the work done by the boy pulling the wagon, we need to use the formula:

Work = Force * Distance * Cosine(angle)

Given:
Force (F) = 65.0 N
Distance (d) = 25.0 m
Angle (θ) = 31.0°

Substituting these values into the formula, we have:

Work = 65.0 N * 25.0 m * Cos(31.0°)

Now, we can calculate the value:

Work = 65.0 N * 25.0 m * Cos(31.0°)

Work = 1625 N*m * Cos(31.0°)

Using a calculator, we can find the cosine of 31.0°, which is approximately 0.8576:

Work = 1625 N*m * 0.8576

Work ≈ 1394.4 Joules

So, the work done by the boy pulling the wagon is approximately 1394.4 Joules.

To determine the amount of work done by the boy pulling his sister in the wagon, we can use the formula for work:

Work = Force * Distance * Cos(θ)

In this case, the force applied by the boy is 65.0 N, and the distance is 25.0 m. However, we also need to consider the angle at which the force is applied. The angle given is 31.0°.

First, we need to find the component of the force in the direction of motion, as that's the only component that contributes to the work. This can be found using trigonometry.

F_parallel = Force * Cos(θ)

where F_parallel is the component of the force in the direction of motion.

Substituting the given values:

F_parallel = 65.0 N * Cos(31.0°)

Next, we can calculate the work using the formula:

Work = F_parallel * Distance

Substituting the values:

Work = (65.0 N * Cos(31.0°)) * 25.0 m

Evaluating this expression will give us the amount of work done by the boy pulling his sister in the wagon.

F' = F*Cos A = 65*Cos31 = 55.7N = Hor. component = Component that pulls the wagon.

Work = F'*d.