A 2- kg block and an 8 kg block are both attached to an ideal spring (for which

Question

A 2- kg block and an 8 kg block are both attached to an ideal spring (for which k=200 N/m. In an initial experiment, a 100-gram (0,1 kg) ball of clay is thrown at the 2-ks block. The clay is moving horizontally with speed v when it hits and sticks to the block. The 8-kg block is held still by a stop. As a result, the spring compresses a max distance of 0.4 m. Calculate the following: a) the energy stored in the spring at max compression b) the speed of the clay ball and 2-kg block immediately after the clay sticks to the block but before the spring compresses significantly. c) the initial speed, v, of the clay.

Explanation / Answer

U = 1/2 k x^2 = 1/2 ( 200 ) ( 0.4)^2 = 16 J

(b)

U = 1/2 mv^2

v = root 2 U/m = root 2( 16)/2.1 kg = 3.9 m/s

(c)

from the conservation of momentum

mv = (m+M) v

v = m+M) v/ m = 2.1( 3.9)/0.1 = 81.9 m/s

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