A load of 981 N is suspended from a steel wire of radius 1 mm. What is

1.	A load of 981 N is suspended from a steel wire of radius 1 mm. What is the maximum angle through which the wire with the load can be deflected so that it does not break when the load passes through the equilibrium position. Breaking stress is 7.85 x 108 Nm-2
Answer» Let θ be the maximum angular deflection them 1/2mv² = mg (l - lcosθ) and T - mg = mv²/l T = mg + mv²/l T/πr² = mg + 2 mg (l - lcosθ) = 3mg - 2mg cosθ For maximum value of θ, stress (=T/πr²) must be equal to breaking stress, i.e., T/πr²= 7.85 x 10⁸ or, (3mg - 2mg cosθ)/(π x (10^-3)²) = 7.85 x 10⁸ or, cosθ = 0.2436 = cos 75.9° or, θ = 75.9°

A load of 981 N is suspended from a steel wire of radius 1 mm. What is the maximum angle through which the wire with the load can be deflected so that it does not break when the load passes through the equilibrium position. Breaking stress is 7.85 x 108 Nm-2

Answer»

Let θ be the maximum angular deflection them

1/2mv² = mg (l - lcosθ)

and T - mg = mv²/l

T = mg + mv²/l

T/πr² = mg + 2 mg (l - lcosθ)

= 3mg - 2mg cosθ

For maximum value of θ, stress (=T/πr²) must be equal to breaking stress,

i.e., T/πr²= 7.85 x 10⁸

or, (3mg - 2mg cosθ)/(π x (10^-3)²) = 7.85 x 10⁸

or, cosθ = 0.2436 = cos 75.9°

or, θ = 75.9°