Problem 245: Crazy crates
Bet you can’t get an angle on this problem.
Ernesto Efficiencia and his partner Brut S. Trength (Mr. T for short) usually work well together in their commercial moving business, Two Men, A Truck, and Some Beer, except when they have a difference of opinion on the best way to get a job done. Some days it’s a truckload of player pianos, other days, a semi full of feather pillows. The excitement never seems to end.
Today’s challenge involves moving a couple hundred orange crates from one side of an old warehouse to the other. Trouble is, Mr. T’s motto is identical to the Nike ad: “Just do it,” while Mr. Efficiencia’s approach is more scientific, because if there’s one thing he can’t stand, it’s wasting energy.
To make matters worse, there’s no dolly or forklift in the dilapidated warehouse, just a tattered old rope. Brut wants to get started pulling the crates to their new position. Ernesto says, “Hold everything!” He wants to figure out the best angle to pull on the rope so they can use the least amount of energy for the job.
As Brut cracks open a cold one, Ernesto ties the rope onto one of the crates. The rope makes an angle, theta, with respect to the floor. The coefficient of friction between the crate and the floor is 0.50 and the crate has a mass of 40 kg. What is the best angle to pull on the rope so Ernesto can apply the minimum force and save his energy?
