Question

Different mass crates are placed on top of springs of uncompressed length L_0 and stiffness k. The crates are released and the springs compress to a length L before bringing the crates back up to their original positions.

Rank the time required for the crates to return to their initial positions from largest to smallest.

1 )
k= 10 n/m
L= 5 cm
L_0= 10 cm

2)
k= 5 n/m
L= 10 cm
L_0= 20 cm

3)
k= 20 n/m
L= 5 cm
L_0= 15 cm

4)
k= 15 n/m
L= 10 cm
L_0= 15 cm

5)
k= 10 n/m
L= 5 cm
L_0= 20 cm

6)
k= 5 n/m
L= 5 cm
L_0= 10 cm

Please explain equation used. Thank you!!

Answer 1

For each example, find the mass of the crate. The mass of the crate will be m such that kx = mg (an equilibrium condition), where x = L_0 - L and g = 9.8 m/s^2. Don't forget to convert x into meters. The period of a mass-spring system is proportional to sqrt(m/k), so the order of systems from longest to least time for recovery will be the same as the order of decreasing m/k, and you will be able to calculate m/k for each system

Answer 2

Here is the correct procedure:

first: find Smax = L0-L

Second: find m=K*Smax/2*9.8

third: find T=2*pi*sqrt(m/k)

That will give you a perfect answer for the period :)

applying this formula you will get: 5>3=2>6=4=1

Answer 3

1.) .5102 2.) 1.02 3.) 1.02 4.) .5102 5.) 1.531 6.) .5102

5>2,3>1,4,6