Mike pulls a 4.5 kg sled across level snow with a force of 250 N along a rope that is 35.0° above the horizontal. If the sled moves a distance of 63.8 m, how much work does Mike do?
Mike pulls a 4.5 kg sled across level snow with a force of 225 N along a rope that is 35.0 degrees above the horizontal. If the sled moves a distance of 65.3 m, how much work does Mike do
To determine the work done by Mike, we can use the formula:
Work = Force * Distance * cos(theta)
Where:
- Force is the magnitude of the force applied by Mike (250 N).
- Distance is the distance over which the sled is moved (63.8 m).
- Theta is the angle between the force applied and the direction of motion (35.0°).
Now, let's calculate the work done by substituting the values into the formula:
Work = 250 N * 63.8 m * cos(35.0°)
To calculate the cosine of 35.0°, use a calculator or reference table:
cos(35.0°) ≈ 0.819
Now, substitute this value to calculate the final answer:
Work ≈ 250 N * 63.8 m * 0.819
Work ≈ 13158.55 J
Therefore, Mike does approximately 13158.55 Joules of work.
To calculate the work done by Mike, we can use the equation:
Work = Force * Distance * cos(theta)
where:
- Work is the amount of work done by Mike
- Force is the applied force by Mike along the rope
- Distance is the distance covered by the sled
- theta is the angle between the direction of the force and the direction of motion
In this case:
- Force = 250 N
- Distance = 63.8 m
- theta = 35.0°
First, we need to find the component of the force in the direction of motion by multiplying the force by the cosine of the angle:
Force component = Force * cos(theta)
Force component = 250 N * cos(35.0°)
Calculating this, we find:
Force component ≈ 250 N * cos(35.0°) ≈ 204.1 N
Now we can calculate the work done by Mike by multiplying the force component by the distance:
Work = Force component * Distance
Work = 204.1 N * 63.8 m
Calculating this, we find:
Work ≈ 13019.2 N·m or 13019.2 J (joules)
Therefore, Mike does approximately 13019.2 J of work.