A uniform plank is supported at its middle…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A uniform plank is supported at its middle. A child sits from the support. Where must a child sit, on the other side, to balance it? Does the plank's own mass matter?
Need a reminder? The key ideaShow
A rigid body is in equilibrium when the net force is zero and the net torque about every point is zero. Take torques about a point where an unknown force acts, so that it drops out.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Torques about the support.
Step 1. , so .
Step 2. The plank. Its weight acts at its middle, right over the support, so it has no torque and does not matter.
Answer: from the support; the plank's mass does not matter.
Check. The lighter child sits farther out, as expected.
Watch out. If the support were not at the middle, the plank's weight would give a torque, and it would matter.
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