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?

Answer 1

a) mg=Kx

==> x= mg/K= 0.284*9.8/58.9 = 0.047 m=4.7 cm

==> L=11+4.7 = 15.7 cm

b) msqrt(g^2 +a^2)= Kx

==>x= m*sqrt(g^2 +a^2)/K=0.284*sqrt(9.8^2+2.23^2)/58.9=0.0484 m= 4.84 cm

==> L=11+4.84 cm = 15.84 cm

Answer 2

mg=kx

x=.284*9.8/.58.9=4.725cm

total length=11+4.725=15.725cm

for second case

Kx= m(a^2+g^2)^.5

x= 4.846cm

total lenght=15.864cm