A 100g block on a frictionless table is firmly attached to one end of a spring with k = 20N/m. ?

Question

A 100g block on a frictionless table is firmly attached to one end of a spring with k = 20N/m. The other end of the spring is anchored to the wall. A 20g ball is thrown horizontally toward the block with a speed of 5.0m/s.
a) If the collision is perfectly elastic, what is the balls speed immediately after the collision?
b) What is the maximum compression of the spring?
c) Repeat parts a and b for the case o perfectly inelastic collision

NCS · Accepted Answer

a) For an elastic, head-on collision, we know (from conservation of energy), that the relative velocity of approach = relative velocity of separation, or
5.0 m/s = u - v

where v is the post-collision velocity of the ball

and u is the post-collision velocity of the block

so
u = v + 5.0m/s

conserve momentum for the collision, substituting for u:
20g*5.0m/s = 20g*v + 100g*(v + 5.0m/s)
solves to
v = -3.33 m/s
and so the ball's speed is 3.33 m/s ◄

b) Then u = 1.67 m/s, and the block's KE gets converted into spring PE:
½ * 0.100kg * (1.67m/s)² = ½ * 20N/m * x²
solves to
x = 0.12 m ◄

c) Now the objects have a common post-collision velocity:
20g*5.0m/s = 120g*v
solves to
v = 0.83 m/s ◄

½*0.120kg*(0.83m/s)² = ½ * 20N/m * x²
solves to
x = 0.065 m ◄

Hope this helps!

A 100g block on a frictionless table is firmly attached to one end of a spring with k = 20N/m. ?

1 Answer