Question

Suppose an adult pulls on the rope of a sled with a force of 85N and at an angle of 26° with the ground. If the sled moves 40 m along the surface of the ground, how much work was done?

Answer 1

To calculate the work done when pulling the sled, we can use the formula for work:

\[
\text{Work} = F \cdot d \cdot \cos(\theta)
\]

Where:
- \( F \) is the force applied (85 N),
- \( d \) is the distance moved in the direction of the force (40 m),
- \( \theta \) is the angle between the force and the direction of motion (26°).

First, we need to find \( \cos(26°) \):

\[
\cos(26°) \approx 0.8988
\]

Now we can substitute the values into the work formula:

\[
\text{Work} = 85 \, \text{N} \times 40 \, \text{m} \times \cos(26°)
\]

Substituting the value for \( \cos(26°) \):

\[
\text{Work} = 85 \, \text{N} \times 40 \, \text{m} \times 0.8988
\]

Calculating it step by step:

\[
\text{Work} = 85 \times 40 \times 0.8988
\]

Calculating \( 85 \times 40 \):

\[
85 \times 40 = 3400
\]

Now multiplying by \( 0.8988 \):

\[
\text{Work} = 3400 \times 0.8988 \approx 3054.72 \, \text{J}
\]

Therefore, the work done on the sled is approximately:

\[
\boxed{3054.72 \, \text{J}}
\]