A child pulls a 3kg sled 200m along the ice by exerting a force of 40N on a rope that makes an angle of 30 degrees with the horizontal. The coefficient of friction between the sled and the ice is 0.15.
a) How much work has the applied force done on the sled?
b) How much work has friction done on the sled?
c) What is the net work done on the sled?
To solve this problem, we need to use the formulas for work done by a force and work done by friction.
a) The work done by the applied force can be calculated using the formula:
Work = Force * Distance * Cos(angle)
W = 40N * 200m * Cos(30 degrees)
W = 40N * 200m * 0.866
W ≈ 6928 Joules
b) The work done by friction can be calculated using the formula:
Work = Force of Friction * Distance
The force of friction can be calculated using the equation:
Force of Friction = Coefficient of Friction * Normal Force
The normal force is equal to the weight of the sled, which can be calculated using the equation:
Normal Force = Mass * 9.8m/s^2
Normal Force = 3kg * 9.8m/s^2
Normal Force = 29.4N
Therefore, the Force of Friction = 0.15 * 29.4N = 4.41N
Now, we can calculate the work done by friction:
Work = 4.41N * 200m
W = 882 Joules
c) The net work done on the sled can be calculated by subtracting the work done by friction from the work done by the applied force.
Net Work = Work by Applied Force - Work by Friction
Net Work = 6928J - 882J
Net Work ≈ 6046J
Therefore, the net work done on the sled is approximately 6046 Joules.