Problem 8.20: Combining Conservation Laws. A 15.0 kg block is atached to a very

Question

Problem 8.20: Combining Conservation Laws. A 15.0 kg block is atached to a very light horizonal spring of force constant 600 N/m and is resting on a smooth horizontal table. (See the figure below 50k Q Tap image to zoom Suddenly it is struck by a 3.00 kg stone traveling horizontally at 8.00 m/s to the right, whereupon the stone rebounds at 2.00 m/s horizontally to the left. Part A Find the maximum distance that the block will compress the spring after the collision.(Hint: Break this problem into two parts - the collision and the behavior after the collision - and apply the appropriate conservation law to each part.) 2.87 m Submit Give Up

Explanation / Answer

m1u1+m2u2 = m1v1 + m2v2

15(0) + 3*8 = 15v + 3*(-2)

v = 2 m/s

Initial velocity of the 15 kg block is 2 m/s

KE = (1/2)mv^2 = 1/2 * 15*2*2 = 30 J

KE is converted into spring energy.

Spring energy for 'x' compression = (1/2)kx^2

(1/2)*600*x^2 = 30

x = 31.62 cm

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