Problem 10.49 Part A A 100 g block on a frictionless table is firmly attached to

Question

Problem 10.49 Part A A 100 g block on a frictionless table is firmly attached to one end of a spring with k 30 N/m The other end of the spring is anchored to the wall. A 29 K ball s thrown horizontally toward the block with a speed of 5.1 m/s If the collision is perfectly elastic, what is the ball's speed immediately after the collision? Express your answer to two significant figures and include the appropriate units. u= 1 Value Units Submit Part B What is the maximum compression of the spring? Express your answer to two significant figures and include the appropriate units. 1&z;= | Value Units

Explanation / Answer

given that

mass of the block M  = 100 g

mass of ball m = 29 g

spring constant k =30 N/m

initial speed of ball vi = 5.1 m/s

final speed of ball

part A

for the elastic collision

vf = (m - M)/(m +M)*vi = (0.029-0.100)/(0.029+0.100)*5.1m/s = -0.3621 / 0.129 = -2.80 m/s

ball's speed after the collision vf = 2.80 m/s (in opposite direction)

block speed

vblock = 2*m/(m+M)*vi = 2*0.029/(0.029+0.100)*5.1 = 2.29 m/s  

part B

from law of energy conservation

1/2*M*vblock2 = 1/2*k*x2

x = sqrt [M*vblock2 /k]

x = sqrt [0.100*2.29*2.29 / 30]

x = 0.132 m

part C

A For a completely inelastic collision

vf = m*vi/(m+M) = 0.029*5.1 / (0.029 +0.100)

vf = 1.14 m/s

partD

from the law of conservation of energy

1/2*(m+M)*vf2 = 1/2*k*x2

x = sqrt [(m+M)*vf2 / k]

x = sqrt [ 0.129*1.14*1.14 / 30]

x = 0.0747 m  

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