5; 1 Loop-the-loop* A small block of mass m starts from rest and slides along a friction­less Ioop-the-loop as shown in the sketch on the next page. What should be the initial height z, so that m pushes against the top of the track (at a) with a force equal to its weight?

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5.3 Ballistic pendulum" , A simple way to, measure the speed of a bullet is with a ballistic ,, , pendulum. As illustrated, this consists of a wooden block of mass , , Minto which the bullet is shot. The block is suspended from cables , " ,, , of length I, and the impact of the bullet causes it to swing through, ,

,)8 la, a maximum angle cp, as shown. The initial speed of the bullet is v, , , and its mass is m..-..-_ ___.._.., !... J (a) How fast is the block moving immediately after the bullet

comes to rest? (Assume that this happens quickly.) (b) Show how to find the velocity of the bullet by measuring

m, M, I, and cp.

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Sliding on a circular path * A small cube of mass m slides down a circular path of radius R cut

I I into a large block of mass M, as shown. M rests on a table, and I both blocks move without friction. The blocks are initially at rest,

and m starts from the top of the path. Find the velocity v of the cube as it leaves the block.

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5.6 Block sliding on a sphere* A small block slides from rest fr h . .of radius R as sh h am t e top of a frictionless sphere

, own on t e next pa H f does it lose contact with the sphere? ,;~. °hw ar below the top x . e sp ere does not move.

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