Answer:
Energy stored in the rod, W = 4.55 × 10⁻⁴ J
Step-by-step explanation:
From the question, the following values are given:
Mass of the brass rod, m = 10kg
Length of rod, l = 1 m
Radius of brass rod, r =1 cm
Change in length of rod, e = ?
Energy stored, W = ?
Young's modulus of brass, Y = 3.5 × 10¹⁰ N/m²
Using the formula for energy stored in an elastic material;
W = 1/2 F × e
Force due to the load, F = mg = 10 × 10 = 100N
To determine the change in length, e, we use the formula for Young's modulus of elasticity;
Y = (F/A)/(e/l) = F × l / A × e
e = (F × l) / (Y × A)
where A = πr²
e = 100 × 1 / (3.5 × 10¹⁰ × π × (0.01)²
e = 9.09 × 10⁻⁶ m
Therefore, energy stored in the rod, W = 1/2 × 100 × 9.09 × 10⁻⁶
Energy stored in the rod, W = 4.55 × 10⁻⁴ J