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:

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