In Greek mythology, Sisyphus was punished by Hades for being deceitful and forced to roll a boulder up a steep hill for eternity. How much force must Sisyphus exert on the boulder to start moving it up the hil as shown in the image below? The coefficient of static friction between the boulder and the surface of the hill is 0.60. 60° 150 kg
The Correct Answer and Explanation is:
Of course. Here is the solution to the physics problem.
Answer:
Sisyphus must exert a force of approximately 1714 Newtons to start moving the boulder up the hill.
Explanation
To find the force Sisyphus must apply, we need to identify and calculate all the forces that oppose the upward motion of the boulder. There are two such forces: the component of the boulder’s weight pulling it down the slope and the force of static friction. Sisyphus must exert a force equal to the sum of these two forces to initiate movement.
First, we calculate the component of gravity acting parallel to the hill. The weight of the boulder is its mass multiplied by the acceleration due to gravity (g ≈ 9.8 m/s²).
Weight (W) = 150 kg * 9.8 m/s² = 1470 N.
This weight acts straight down, but on a 60° incline, only a component of this force pulls the boulder down the slope. This component is calculated using the sine of the angle:
Force of gravity down the slope (Fg_parallel) = W * sin(60°) = 1470 N * 0.866 ≈ 1273 N.
Second, we calculate the force of static friction. This force resists the start of motion and is calculated by multiplying the coefficient of static friction (μs) by the normal force (N). The normal force is the component of the boulder’s weight acting perpendicular to the hill’s surface. It is calculated using the cosine of the angle:
Normal Force (N) = W * cos(60°) = 1470 N * 0.5 = 735 N.
Now we can find the maximum static friction force (Ff):
Friction Force (Ff) = μs * N = 0.60 * 735 N = 441 N.
Finally, to start moving the boulder, Sisyphus must push with a force that overcomes both the parallel component of gravity and the static friction.
Total Force Required = Fg_parallel + Ff
Total Force Required = 1273 N + 441 N = 1714 N.
Therefore, Sisyphus must exert a force of 1714 N parallel to the hill to begin his eternal task.
