- #1
mattbeatlefreak
- 34
- 2
Homework Statement
A 4.5-kg bowling ball is perched on a concrete ledge directly below your dorm room window, with the side of the ball opposite the holes touching the wall. Wanting to hold the ball in place so that it doesn't roll off and land on somebody, you manage to hook one of the holes with a wire and exert a purely tangential (and vertical) force on the ball. The coefficient of static friction between ball and ledge is the same as that between ball and wall, μs = 0.43. What is the maximum upward force you can exert so that the ball does not rotate and you lose your hold? Even though the ball has holes drilled in it, assume a uniform distribution of inertia.
Homework Equations
τ = Fr
F = ma
ƒ = μN
The Attempt at a Solution
I drew a diagram and wrote equations for net torque, net force in x direction, and net force in y direction.
τnet=T-ƒwall-ƒledge=0
Fx=ƒledge-Nwall=0
Fy=T-mg+Nledge+ƒwall=0
To find the maximum force, I set the frictional force from the wall = μ times the normal force from the ledge. Also, I set the frictional force from the ledge = μ times the normal force from the wall.
Substituting values:
T-.43Nledge-.43Nwall=0
.43Nwall-Nwall=0
T-44.1+Nledge+.43Nledge=0
Solving for Nwall gave a value of 0, which doesn't seem correct. Continuing through regardless, I finished with an answer of 10.2 N for the tension, which wasn't correct.