Question

The spring constant of Spring A is twice as great as the spring constant of Spring B. Both springs are stretched the same amount. How does the

force the Spring A applies compare to the force Spring B applies?

Answer 1

The force
`F_A` needed to stretch spring A is going to be twice as much as the force
`F_B` needed to stretch spring B.

Step-by-step explanation:

We know that the spring constants are related as

`k_A = 2k_B`

The force
`F_A` needed to stretch spring A is given by

`F_A = -k_Ax`

Also, the force
`F_B` needed to stretch spring is

`F_B = -k_Bx`

Taking the ratio of the forces, we get

`(F_A)/(F_B) = (-k_Ax)/(-k_Bx) = (k_A)/(k_B)`

Since
`k_A = 2k_B,` the equation above becomes

`(F_A)/(F_B) = (2k_B)/(k_B) = 2`

or

`F_A = 2F_B`

This shows that since the spring constant of spring A is twice as large as that of spring B, the force needed is going to be twice as large.

Answer 2

FA = 2FB

Force on spring A is twice the Force on spring B

Step-by-step explanation:

F = kx

FB = (kB)x

FA = (kA)x

FA= (2kB)x

FA = 2(kB)x

FA = 2FB