Diego pulls a 4.5 kg sled across level snow with a force, F, of 200 N on a rope that is 35.0° above the horizontal. If the sled moves a distance of 67.5 m, how much work does Diego do?
Fh = 200*cos(35) = 163.83N.
W = Fh*D = 163.83*67.5m=11059 Joules.
To find the work done by Diego, we can use the formula:
Work (W) = Force (F) * Distance (d) * cos(theta)
Where:
- Force (F) is the magnitude of the force applied by Diego, which is 200 N.
- Distance (d) is the distance the sled moves, which is 67.5 m.
- theta is the angle between the direction of the force and the direction of movement, which is 35.0°.
First, we need to convert the angle from degrees to radians. We know that 180° = π radians, so:
35.0° * (π/180°) = 0.6109 radians
Now we can substitute the values into the formula:
W = 200 N * 67.5 m * cos(0.6109 radians)
To find the cosine of the angle, we can use a scientific calculator or use the cosine table.
Let's assume that the cosine of 0.6109 radians is approximately 0.797.
W = 200 N * 67.5 m * 0.797
Now, we can calculate the value of the work:
W ≈ 10754.5 joules
Therefore, Diego does approximately 10754.5 joules of work.