springs A and B are identical except that A is stiffer than B i e the force constant is - Physics - Work energy power

Question

springs A and B are identical except that A is stiffer than B i
e the force constant is k(A) k(B) in which spring is more work done
if:
1 they stretch by same amount
2 they are stretched by same force

Himanshu · Accepted Answer

(2) When they are stretched by the same force.

In this case F (Force is the same)

$F_{A} = k_{A} x_{A} = F F_{B} = k_{B} x_{B} = F W_{A} = \frac{1}{2} k_{A} x_{A}^{2} W_{B} = \frac{1}{2} k_{B} x_{B}^{2} \frac{W_{A}}{W_{B}} = \frac{k_{A} \times \frac{F^{2}}{k_{A}^{2}}}{k_{B} \times \frac{F^{2}}{k_{B}^{2}}} = \frac{k_{B}}{k_{A}} \Rightarrow W_{A} < W_{B}$

(1) When stretched by the same amount, i.e. the extensions in both the springs is the same.

$\frac{W_{A}}{W_{B}} = \frac{\frac{1}{2} k_{A} x_{A}^{2}}{\frac{1}{2} k_{B} x_{B}^{2}} = \frac{k_{A}}{k_{B}} \Rightarrow W_{A} > W_{B}$

springs A and B are identical except that A is stiffer than B i.e. the force constant is k(A) k(B) . in which spring is more work done if: 1. they stretch by same amount 2. they are stretched by same force

springs A and B are identical except that A is stiffer than B i.e. the force constant is k(A) k(B) . in which spring is more work done if:

1. they stretch by same amount

2. they are stretched by same force