A 0.60 kg bob hangs on a string 1.5 m long.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A bob hangs on a string long. It is pulled aside until the string makes with the vertical, and let go. Taking , find
- its speed at the lowest point;
- the tension in the string there.
Need a reminder? The key ideaShow
When only conservative forces (gravity, springs) do work, mechanical energy is conserved: . Forces that do no work, like a smooth surface's push or a string at right angles to the motion, do not spoil it.
On a curved path, use energy for the speed and toward the centre for the forces. At the top of a loop the track's push and the weight both point down: , and the cart stays on while .
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. , , .
Plan. Energy for the speed; Newton's second law toward the centre for the tension.
Step 1. Drop. .
Step 2. Speed. .
Step 3. Tension. .
Answer: (a) . (b) .
Check. The formula agrees.
Watch out. At the bottom the tension is more than the weight: it must also pull the bob round the circle.
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