A spring has an equilibrium length of 11.0 cm and a spring constant of 58.9 N/m.

Question

A spring has an equilibrium length of 11.0 cm and a spring constant of 58.9 N/m. The spring is connected to the underside of the roof of a car and a 0.284 kg block suspended from it. How long (in cm) is the spring when the car is at rest?

How long is the spring if the car is accelerating horizontally at 2.23 m/s2?

Separate problem

A coil spring is extended by 3.2 cm when it supports a 1.00- N weight. If an identical spring is joined to the end of the first one, what is the extension of the combined spring when it supports the same 1.00- N weight? Assume the spring masses to be negligible.

Explanation / Answer

1.

By Conservation of energy

(1/2)*K*X^2=m*g*X

(1/2)*58.9*X =0.284*9.8

X=9.45 cm

Total Length of spring is

L=9.45+11

L=20.45 cm

2.

spring constant

F=KX

1=K*0.032

K=31.25 N/m

For identical springs connected in series

1/Keq =1/K1 +1/K2 =1/31.25 +1/31.25

Keq=15.625 N/m

so extension of combined spring is

X=F/K =1/15.625

X=0.064 m or 6.4 cm

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