Step 1: Formula for Elongation
The amount a wire stretches depends on Young's modulus formula:
Y=‌=‌Step 2: What stays the same?
Both wires are made of the same material, have the same length, and the same stretching force. This means their Young's modulus
(Y), original length
(l), and force
(F) are the same.
Step 3: Setting up the equation for both wires
Since Young's modulus is the same for both wires, we set the formulas equal for each wire:
Y1=Y2‌=‌Step 4: Rearranging to compare elongations
We can simplify to find how the elongation (
∆l ) relates to diameter (
d ):
∆l1⋅d12=∆l2⋅d22So,
∆l2=∆l1⋅(‌)2Step 5: Substitute values
We are told
∆l1=1mm (the first wire stretches 1 mm ) and
d2=4d1 (the second wire's diameter is 4 times bigger).
∆l2=1⋅(‌)2=1⋅(‌)2=‌mmFinal Answer
The second, thicker wire stretches only
‌mm when the same force is applied.
