A-Level AQA Physics The Young Modulus: Two wires P and Q are made of th

Two wires P and Q are made of the same material and have the same cross-sectional area - AQA - A-Level Physics - Question 28 - 2022 - Paper 1

Question 28

Two wires P and Q are made of the same material and have the same cross-sectional area. P has an original length L and is subject to a tensile force F. P extends a ... show full transcript

Worked Solution & Example Answer:Two wires P and Q are made of the same material and have the same cross-sectional area - AQA - A-Level Physics - Question 28 - 2022 - Paper 1

Step 1

A. The stress in P and the stress in Q are the same.

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Answer

To determine if the stress is the same in both wires, we use the formula for stress:

$\text{Stress} = \frac{\text{Force}}{\text{Area}}$

For wire P, the stress is ( \frac{F}{A} ). For wire Q, the stress is ( \frac{2F}{A} ). Thus, the stress in Q is double that in P, making this statement incorrect.

Step 2

B. The extension of Q is 2x.

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Answer

Using Hooke's Law, the extension ( \Delta L ) can be calculated as:

$\Delta L = \frac{FL}{AY}$

For wire P: $\Delta L_P = \frac{F \cdot L}{A \cdot Y} = x$

For wire Q, substituting the lengths and forces: $\Delta L_Q = \frac{2F \cdot 2L}{A \cdot Y} = \frac{4FL}{AY} = 4x$

Therefore, the extension of Q is not 2x, making this statement incorrect.

Step 3

C. The strain of Q is double the strain of P.

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Answer

Strain is defined as the ratio of extension to original length:

$\text{Strain} = \frac{\Delta L}{L}$

For wire P: $\text{Strain}_P = \frac{x}{L}$

For wire Q: $\text{Strain}_Q = \frac{4x}{2L} = \frac{2x}{L}$

This shows that the strain of Q is indeed double the strain of P, therefore this statement is correct.

Step 4

D. The value of stress for P is half that of Q.

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Answer

From our earlier calculations:

Stress in P: ( \text{Stress}_P = \frac{F}{A} )
Stress in Q: ( \text{Stress}_Q = \frac{2F}{A} )

Thus, ( \text{Stress}_P = \frac{1}{2} \text{Stress}_Q ), indicating that the stress for P is half that of Q. This statement is correct.

Two wires P and Q are made of the same material and have the same cross-sectional area - AQA - A-Level Physics - Question 28 - 2022 - Paper 1

Worked Solution & Example Answer:Two wires P and Q are made of the same material and have the same cross-sectional area - AQA - A-Level Physics - Question 28 - 2022 - Paper 1

A. The stress in P and the stress in Q are the same.

B. The extension of Q is 2x.

C. The strain of Q is double the strain of P.

D. The value of stress for P is half that of Q.

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