Question

A spring has an equilibrium length of 20.0 cm and a spring constant of 59.9 N/m. The spring is connected to the underside of the roof of a car and a 0.204 kg block suspended from it.

A) How long (in cm) is the spring when the car is at rest?

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

Answer 1

apply F = kx

x = 0.204*9.8/59.9

x = 3.33cm

length = 20+3.33 = 23.33 cm

b. when a = 2.23m/s^2

F = kx = ma

x     = 0.204*2.23/59.9

x   =0.75 cm

so length L = 23.33+0.75 = 24.08 cm

Answer 2

A)
weight of block is balanced by spring force
mg=kx
0.204*9.8=59.9*x
x=0.03338m
=3.338 cm

New ength =20+3.338=23.338 cm
B)
netforce on block is balanced by spring force
sqrt(m(g^2+a^2))=kx
sqrt(0.204^2(9.8^2+2.23^2))=59.9*x
x=0.03423m

x=3.423 cm

New length =20+3.423=23.423 cm