A mirror of mass 2.6 kg hangs from a wire passed over a nail.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A mirror of mass hangs from a wire passed over a nail. Each half of the wire makes with the vertical. Taking :
- What is the tension in the wire?
- The wire is shortened so that each half makes with the vertical. What is the tension now?
Need a reminder? The key ideaShow
A body at rest is in equilibrium: the forces on it balance along every direction. Split each slanting force into parts:
A string pulls along its own length; a light string over a smooth nail has the same tension on both sides.
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.
Given. , so .
Plan. The horizontal parts of the two pulls cancel. The vertical parts hold up the weight.
Step 1. (a) , so .
Step 2. (b) .
Answer: (a) . (b) .
Check. A flatter wire has a smaller upward part for each newton of tension, so it needs more tension. The answer grew, as it should.
Watch out. The angle is with the vertical, so the upward part is , not .
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