A person pulls a toboggan for a distance of 30.0 m along the snow with a rope directed 20.0° above the snow. The tension in the rope is 85.0 N.
(a) How much work is done on the toboggan by the tension force?
F=85*cos20 N
work=fd= 85*cos20*30
work =2,4 kNm
To find the work done on the toboggan by the tension force, we can use the formula:
Work = Force * Distance * cos(theta)
where:
Work is the work done on the toboggan
Force is the tension in the rope
Distance is the distance over which the force is applied
theta is the angle between the direction of the force and the direction of motion
In this case, we are given:
Force = 85.0 N
Distance = 30.0 m
theta = 20.0°
Now, we can substitute these values into the formula to calculate the work done on the toboggan:
Work = 85.0 N * 30.0 m * cos(20.0°)
To get the answer, we need to calculate the cosine of 20.0° and then multiply it by the force and distance:
cos(20.0°) = 0.9397 (rounded to four decimal places)
Work = 85.0 N * 30.0 m * 0.9397
Simplifying the expression further:
Work ≈ 2396.405 J
Therefore, the work done on the toboggan by the tension force is approximately 2396.405 Joules.