A person pulls a toboggan for a distance of 40.0 m along the snow with a rope directed 15.0° above the snow. The tension in the rope is 69.0 N.
(a) How much work is done on the toboggan by the tension force?
(b) How much work is done if the same tension is directed parallel to the snow?
(a) 69 * 40 * cos 15 = __ Joules
(b) 69 * 40 = __ Joules
To calculate the work done on the toboggan, we can use the formula:
Work = Force x Distance x cos(angle)
Where:
- Work is the amount of work done on the toboggan
- Force is the tension in the rope
- Distance is the distance traveled by the toboggan
- Angle is the angle between the force and the direction of motion
(a) How much work is done on the toboggan by the tension force?
In this case, the tension force is directed 15.0° above the snow. Therefore, we can calculate the work done as follows:
Work = 69.0 N x 40.0 m x cos(15.0°)
Now let's calculate it:
Work = 69.0 N x 40.0 m x cos(15.0°)
Work ≈ 2815.62 joules
Therefore, the work done on the toboggan by the tension force is approximately 2815.62 joules.
(b) How much work is done if the same tension is directed parallel to the snow?
If the tension force is directed parallel to the snow, the angle between the force and the direction of motion is 0°. Therefore, the formula for calculating work becomes:
Work = Force x Distance x cos(0°)
Since cos(0°) = 1, the formula simplifies to:
Work = Force x Distance
Now let's calculate it:
Work = 69.0 N x 40.0 m
Work = 2760 joules
Therefore, if the same tension is directed parallel to the snow, the work done on the toboggan is 2760 joules.