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A copper wire of diameter 1.0 cm stretches 1.0% when it is used to lift a load upward with an acceleration of 2.0 m/s^2. What is the weight of the load?

A) 1.96 × 10^3 N
B) 9.8 × 10^3 N
C) 1.96 × 10^4 N
D) 9.8 × 10^4 N

1 Answer

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Final answer:

if A copper wire of diameter 1.0 cm stretches 1.0% when it is used to lift a load upward with an acceleration of 2.0 m/s^2. The weight of the load is 4.71 N. None of the provided options are correct.

Step-by-step explanation:

To find the weight of the load, we need to first calculate the force exerted by the wire when it stretches. The stretching of the wire is given as 1.0% which corresponds to a strain of 0.01. Since Young's modulus (E) is a measure of a material's stiffness, we can use it to relate the stress (σ) in the wire to the strain (ε) using the formula σ = E × ε. The stress is equal to the force (F) divided by the cross-sectional area (A) of the wire, so we can rearrange the equation to solve for the force:

F = σ × A

where σ = E × ε is the stress, E is Young's modulus, and ε is the strain. The cross-sectional area (A) of the wire can be calculated using the formula A = π × r^2, where r is the radius of the wire. In this case, the diameter is given as 1.0 cm, so the radius is 0.5 cm (or 0.005 m).

Plugging in the values, we have:

  1. Stress (σ) = (6.00 × 10^6 N/m^2) × (0.01) = 6.00 × 10^4 N/m^2

  2. Cross-sectional area (A) = π × (0.005 m)^2 = 7.85 × 10^-5 m^2

Now we can calculate the force (F):

  1. F = (6.00 × 10^4 N/m^2) × (7.85 × 10^-5 m^2) = 4.71 N

Therefore, the weight of the load is approximately 4.71 N. None of the provided options are correct.

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