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17 votes
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?

User Hudvoy
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3.1k points

2 Answers

22 votes
22 votes

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.

User Erikreed
by
2.6k points
21 votes
21 votes

Answer:

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

User Mustafa Deniz
by
2.3k points