Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A block lies on a smooth slope at . A string joins it, over a smooth pulley at the top, to a block that hangs freely. Taking , find the acceleration and the tension.
Bodies joined by a light, taut string (or pushing on each other) move with the same acceleration. First treat the whole system: . Then take one body alone to find the force between them.
On a slope at angle , split the weight: down the slope and into it, so . Sliding down a rough slope, friction acts up it:
A body at rest starts to slide when .
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. On the slope , ; hanging .
Plan. Compare the two pulls along the string, then take the hanging block alone for .
Step 1. The two pulls. Hanging: . Down the slope: . The hanging block wins and falls.
Step 2. Acceleration. .
Step 3. Tension. For the hanging block, : .
Answer: , and .
Check. The slope block: , and . It agrees.
Watch out. Only the part of the weight along the slope, , pulls against the string. The rest is held by the slope.
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