The following are a bunch of pulley exercises and problems. If you can work through and understand them you should be able to solve most standard pulley problems.
The Usual Pulley Assumptions
When working through pulley problems in Engineering Dynamics, we will usually make the following assumptions.
- We can neglect the mass of the pulley.
- We can neglect friction in the pulley’s bearing.
- We can neglect the mass of the rope/string/cord/cable.
- The rope/string/cord/cable does not stretch.
The following video explains how these assumptions make solving pulley problems easier.
Unless stated otherwise, we will regard these assumptions as valid.
Here’s a simple problem that serves as a springboard to learning how to solve pulley problems.
We work through the answer in the video below.
With just a little extra work it is possible to determine the tension too. The tension might be surprising.
Here is a classical pulley problem that asses your understanding of basic mechanics concepts. It is a multiple choice problem. I’m not particularly interested in how you answer. I’m more interested in whether you can form a rigorous argument, based on Newton’s Second Law.
Here’s a video outlining how I solve the problem.
Now for a real pulley problem
Here’s a real pulley problem that requires one to do some real kinematic analysis of the pulley.
In Part A below, we draw free body diagrams, write equations of motion, and begin working out the pulley kinematics.
In Part B, we finish the pulley kinematics and solve for the acceleration.
A thought-provoking pulley problem
Here’s a pulley problem that makes you think more deeply about the pulley kinematics recipe presented in the previous video. It also make you think more deeply about whether a pulley problem is well posed or not.
Here is Part 1 of the video solution. In it, I derive equations of motion, and work out the pulley kinematics.
In Part 2, I solve for tension and interpret the result.