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Work Energy Theorem

Two springs ...

Question

Two springs $A$ and $B$ are identical but $A$ is harder than $B (k_{A} > k_{B})$ . On which spring more work will be done if: (a)They are stretched through the same distance (b)They are stretched by same force?

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Solution

Given $k_{A} > k_{B}$
Case (a) Stretched through same distance $x$ .
Work done by spring $A$ , $W_{A} = \frac{1}{2} k_{A} x^{2}$
Work done by spring $B$ , $W_{B} = \frac{1}{2} k_{B} x^{2}$
$∴ W_{A} > W_{B}$
Case (b) Stretched by same force $F$
Let spring $A$ is stretched by $x_{A}$ and spring $B$ is stretched by $x_{B}$ .
Force $F = k_{A} x_{A} = k_{B} x_{B}$ $\Rightarrow x_{A} < x_{B}$
Work done by spring $A$ , $W_{A} = F x_{A}$
Work done by spring $B$ , $W_{B} = F x_{B}$
$∴ W_{A} < W_{B}$

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Similar questions

A

B

are identical but

A

B (k_{A} > k_{B})

W_{A}

W_{B}

represent the work done when the springs are stretched through the same of the distance and

W_{A}^{'}

W_{B}^{'}

are the work done when these are stretched by equal forces then which of the following is true:

Q. Two springs A and B are identical except that A is stiffer than B i.e.,

k_{A} > k_{B}

. If the two springs are stretched by the same force, then

Q. Two springs have force constants

k_{1}

k_{2} (k_{1} > k_{2})

. On which spring is more work done, if (i) they are stretched by the same force and (ii) they are stretched by same distance?

Q. Two springs A and B are identical except that A is stiffer than B i.e.,

k_{A} > k_{B}

. If the two springs are stretched by the same force, then

Q. If two springs

S_{1}

S_{2}

of force constants

k_{1}

k_{2}

respectively, are stretched by the same force, it is found that more work is done on spring

S_{1}

S_{2}

.

Statement-1: If stretched to the same extension, work done on

S_{1}

, will be more than that on

S_{2}

k_{1} < k_{2}

Choose the correct option.

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