A person pulls a toboggan for a distance of 37.2 m along the snow with a rope directed 25.4° above the snow. The tension in the rope is 84.1 N. How much work is done on the toboggan by the tension force?
Work equals
(distance pulled) x (component of pulling force along the direction of motion)
= 37.2 * 84.1 cos 25.4 Joules
To find the work done on the toboggan by the tension force, we need to use the formula:
Work = Force × Distance × cos(θ)
Where:
Work is the amount of work done (in joules),
Force is the magnitude of the force applied (in newtons),
Distance is the distance over which the force is applied (in meters), and
θ (theta) is the angle between the force and the displacement vector.
In this case, the force applied is the tension in the rope, which is given as 84.1 N. The distance over which the force is applied is 37.2 m.
However, in order to use the formula, we need to determine the angle θ between the force and the displacement vector.
The problem states that the rope is directed 25.4° above the snow. From this information, we can deduce that the angle between the force and the horizontal direction is 90° - 25.4° = 64.6°. Since the tension force is directed upward at an angle above the snow, we can assume that the displacement direction is also along the snow, horizontally.
Therefore, substituting the values into the formula:
Work = 84.1 N × 37.2 m × cos(64.6°)
Calculating this expression will give you the amount of work done on the toboggan by the tension force.