Could someone please double check my logic for question 3c?

https://pmt.physicsandmathstutor.com/download/Admissions/ENGAA/Papers/ENGAA%202017%20Section%202.pdf

k ∝ A/L, where k is spring constant, A is cross sectional area, and L is length.

so if L halves, then k doubles.

then using young modulus equation, E = FL/AX, where E is young modulus, F is force, X is extension

if L halves, then since F and A are constant, X must halve.

Energy equation = 1/2 * k * X^2, so if k doubles and X halves, the energy must halve.

so its U/2 = 1/2mv^2, thus answer is B

https://pmt.physicsandmathstutor.com/download/Admissions/ENGAA/Papers/ENGAA%202017%20Section%202.pdf

k ∝ A/L, where k is spring constant, A is cross sectional area, and L is length.

so if L halves, then k doubles.

then using young modulus equation, E = FL/AX, where E is young modulus, F is force, X is extension

if L halves, then since F and A are constant, X must halve.

Energy equation = 1/2 * k * X^2, so if k doubles and X halves, the energy must halve.

so its U/2 = 1/2mv^2, thus answer is B

Original post by mosaurlodon

Could someone please double check my logic for question 3c?

https://pmt.physicsandmathstutor.com/download/Admissions/ENGAA/Papers/ENGAA%202017%20Section%202.pdf

k ∝ A/L, where k is spring constant, A is cross sectional area, and L is length.

so if L halves, then k doubles.

then using young modulus equation, E = FL/AX, where E is young modulus, F is force, X is extension

if L halves, then since F and A are constant, X must halve.

Energy equation = 1/2 * k * X^2, so if k doubles and X halves, the energy must halve.

so its U/2 = 1/2mv^2, thus answer is B

https://pmt.physicsandmathstutor.com/download/Admissions/ENGAA/Papers/ENGAA%202017%20Section%202.pdf

k ∝ A/L, where k is spring constant, A is cross sectional area, and L is length.

so if L halves, then k doubles.

then using young modulus equation, E = FL/AX, where E is young modulus, F is force, X is extension

if L halves, then since F and A are constant, X must halve.

Energy equation = 1/2 * k * X^2, so if k doubles and X halves, the energy must halve.

so its U/2 = 1/2mv^2, thus answer is B

I see no mistakes in your logic. When you have one or more constants, you need to change the alterable units in equations in the same amount to balance them, as they are proportional to each other. In your cases:

E ~ X (for F and A constants)

Energy ~ X (for k constant)

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