Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

Art!

The abstract sculpture shown in the figure above contains a cube of mass m and sides of length b. The cube rests on top of a cylinder, which is off-center by a distance a. Find the tension in the cable.

There are four forces on the cube: a gravitational force mg, the force FT from the cable, the upward normal force from the cylinder, FN, and the horizontal static frictional force from the cylinder, Fs.

The total force on the cube in the vertical direction is zero:

FN - mg = 0 .

As our axis for defining torques, it's convenient to choose the point of contact between the cube and the cylinder, because then neither Fs nor FN makes any torque. The cable's torque is counterclockwise, and the torque due to gravity is clockwise. and the cylinder's torque is clockwise. Letting counterclockwise torques be positive, and using the convenient equation τ = rF, we find the equation for the total torque:

bFT - FNa = 0 .

We could also write down the equation saying that the total horizontal force is zero, but that would bring in the cylinder's frictional force on the cube, which we don't know and don't need to find. We already have two equations in the two unknowns FT and FN, so there's no need to make it into three equations in three unknowns. Solving the first equation for FN = mg, we then substitute into the second equation to eliminate FN, and solve for FT = (a/b)mg.




Last Update: 2010-11-11