Question

If 3 rods are subjected to stress, the stress on rod 1 and rod 2 are the same and made of the same material. The strain on rod 3 is equal to the strain on rod 1 times the reciprocal of strain on rod 2. Find Young's modulus for rod 3 if the stress is 1500 N/m²? a) 1500 N/m² b) 1000 N/m² c) 2000 N/m² d) 750 N/m²

Answer 1

Young's modulus for rod 3 is the same as rods 1 and 2 since stress and strain are the same, giving us the correct answer as 1500 N/m².

Step-by-step explanation:

To determine Young's modulus for rod 3, we initially acknowledge that since rod 1 and rod 2 are of the same material and the stress is the same on both, the strain will also be the same. For rod 3, the given condition is that its strain equals the strain on rod 1 times the reciprocal of the strain on rod 2. Therefore, the strain on rod 3 will be equivalent to that of rod 1 as the reciprocal of rod 2's strain cancels out with that strain, because they are equal.

Young's modulus (Y) is defined as the ratio of stress (σ) to strain (ε). Based on this definition and given that the stress on rod 3 is 1500 N/m², and the strain is the same as the strain on rod 1 and rod 2:

Y = σ / ε

Since the strain is equal for all three rods and rod 3 has the same stress as rod 1 and rod 2, the Young's modulus for rod 3 is the same as for rod 1 and rod 2.

Therefore, the correct answer is: a) 1500 N/m².

Answer 2

The Young's modulus for rod 3 can be found using the given stress on rod 1 and rod 2 and their corresponding strain values.

Step-by-step explanation:

According to the information given, the stress on rod 1 and rod 2 is the same and made of the same material. Let's assume the stress on rod 1 and rod 2 is represented as S. The strain on rod 3 is equal to the strain on rod 1 multiplied by the reciprocal of the strain on rod 2. Let's assume the strain on rod 1 is represented as E1 and the strain on rod 2 is represented as E2.

From the formula for stress, Stress = Young's modulus × Strain, we can rearrange it to find Young's modulus:

You can use the formula:

Young's modulus (E) = Stress (S) / Strain (E)

Plugging in the given values, we have:

You = 1500 N/m² / E2

Given that S = 1500 N/m², we can substitute it into the formula:

You = 1500 N/m² / E2