A 1 meter long rod of diameter 1 cm supports a hanging mass of 10^4kg. The rod stretches by 6.2 mm. What is Young's modulus for the rod?
To find Young's modulus for the rod, we can use the equation:
Young's modulus (Y) = (F/A) / (ΔL/L)
Where:
- F is the force applied (weight of the hanging mass),
- A is the cross-sectional area of the rod,
- ΔL is the change in length of the rod,
- L is the original length of the rod.
First, let's calculate the force applied (F):
F = m * g
Where:
- m is the mass of the hanging object,
- g is the acceleration due to gravity (approximately 9.8 m/s²).
Given that the mass (m) is 10^4 kg, the force (F) can be calculated as:
F = 10^4 kg * 9.8 m/s²
Next, we need to calculate the cross-sectional area (A) of the rod. The diameter of the rod is 1 cm, so the radius (r) will be half of that:
r = 1 cm / 2 = 0.5 cm = 0.005 m
The cross-sectional area (A) of the rod is given by:
A = π * r²
Substituting the value of the radius (r), we can find the cross-sectional area (A).
Now, let's calculate the change in length (ΔL). We are given that the rod stretches by 6.2 mm, which is 6.2 * 10^-3 m.
Finally, we need to find the original length (L) of the rod. Given that the rod is 1 meter long, our value for L is 1 meter.
Now we have all the values needed to calculate Young's modulus (Y). Plugging in the values into the formula:
Y = (F/A) / (ΔL/L)
Substitute the calculated values of F, A, ΔL, and L into the formula, then compute the expression to find the value of Young's modulus (Y).