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, as shown in Figure 10-18. If the sled moves a distance of 63.6 m, how much work does Diego do?
The component of force in the direction of the movement is 200cos35
multiply that by the distance, and you have the work in joules.
To determine the amount of work that Diego does, we need to use the formula:
Work = Force × Distance × cos(θ)
Where:
- Force (F) is the component of the force acting parallel to the displacement of the sled.
- Distance is the displacement of the sled.
- θ is the angle between the force and the displacement.
In this case, we have the force F = 200 N and the angle θ = 35.0° above the horizontal. However, we need to find the component of the force acting parallel to the displacement to calculate the work.
To find that component, we can use trigonometry. The component of the force acting parallel to the displacement is given by:
Force parallel = Force × cos(θ)
Once we have the parallel force, we can calculate the work using the formula above.
Let's proceed with the calculation:
Force parallel = 200 N × cos(35.0°)
Force parallel = 200 N × 0.819
Force parallel = 163.8 N
Now that we have the force parallel to the displacement, we can calculate the work:
Work = Force parallel × Distance
Work = 163.8 N × 63.6 m
Work ≈ 10,407.68 Joules
Therefore, Diego does approximately 10,407.68 Joules of work.