9. (10 points) A block of mass M = 15kg is attached to a very light horizontal s

Question

9. (10 points) A block of mass M = 15kg is attached to a very light horizontal spring of force constant k = 200.0 N/m and is resting on a frictional horizontal table. Suddenly it is struck by a projectile of mass m = 3.0kg traveling horizontally at vi= 8.0m/s to the right. The projectile is embedded into the block. (a) (3 points) Find the speed of the block and projectile just after they collide A. 1.33m/s B. 3.12m/s C. 4.57m/s D. 31.36m/s (b) (4 points) Find the distance the spring compresses before the combined masses come to a stop. A. 0.16m B. 0.4m C. 1.33m D. 16.5m (c) (3 points) If the projectile had hit the block but then recoiled, would the speed of the block be different from the answer in part (a) A. the block's speed would be larger B. the block's speed would be unchanged C. the block's speed would be smaller

Explanation / Answer

a)

Here , using conservation of momentum ,

(M +m)*v = m*vx

(15 + 3)*v = 3*8

v = 1.33 m/s

speed of block and projectile is 1.33 m/s

b)

Here , Using conservation of momentum ,

0.5kx^2 = 0.5*(M + m )v^2

0.5 * 200 * x^2 = 0.5(18)*1.33^2

x = 0.4 m

the distance spring compress is 0.4 m

c)

C. the speed of speed is smaller

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