A spring with spring constant k = 55 N/m and unstretched length of L 0 = 2.1 is

Question

A spring with spring constant k = 55 N/m and unstretched length of L0 = 2.1 is attached to the ceiling. A block of mass m = 2.5 kg is hung gently on the end of the spring.

1. How far does the spring stretch?

2. Now the block is pulled down until the total amount the spring is stretched is twice the amount found in the above question. The block is then pushed upward with an initial speed vi = 3.5 m/sec. What is the maximum speed of the block?

A spring with spring constant k = 55 N/m and unstretched length of L0 = 2.1 is attached to the ceiling. A block of mass m = 2.5 kg is hung gently on the end of the spring. 1. How far does the spring stretch? 2. Now the block is pulled down until the total amount the spring is stretched is twice the amount found in the above question. The block is then pushed upward with an initial speed vi = 3.5 m/sec. What is the maximum speed of the block?

Explanation / Answer

1,after attaching the 2.5kg mass, you have two forces acting. The force of the spring going up and the force of gravity going down. Then there will be a point where the spring+mass will be in equilibrium.

F(s)-F(g) =0, equal to 0 since equilibrium
F(s) = F(g)
kx=mg
(55)x=(2.5)*9.8
x=0.445 m = 44.5 cm

44.5+2.1=46.6 cm, it will line up at the 46.6cm mark

c) v=5.3

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