8) A 15 kg block is attached to a very light horizontally oriented spring of for

Question

8) A 15 kg block is attached to a very light horizontally oriented spring of force constant k = 500 N/m and is resting on a frictionless surface, as shown Fig.-3. Fig.-3: Problem 8 schematic. The 15 kg mass is suddenly struck by a 3 kg mass moving horizontally to the right with speed v = 8 m/s. After hitting the 15 kg mass, the 3 kg mass rebounds to the left with speed y = 2 m/s. Calculate the maximum distance that the spring is compressed (by the 15 kg mass, after the collision. Choose one of the closest answers shown below. a) 2.57m; b) 0.123m; c) 1.02 m; or d) 0.346m

Explanation / Answer

apply change in KE = Elastic Pot energy

0.5 m (V^2-u^2) = 0.5 Kx^2   = mgh

so

uise m1u1 + m2u2 =     m1v1 + m2v2

3*8 + 0 = -3* 2 + m2v2

v2 = 24 +6)/(15)

v2 = 2 m/s

now use 0.5 K x^2 = 0.5 mv^2

x^2 = 15 * 2*2/(500)

X^2 = 0.12

x = compression = 0.346 m------------<<<<<Answer

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