A truck is pulling a car out of a ditch by means of a steel cable that

1.	A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is 800 N. How much has the cable stretched? (Young’s modulus for steel is 2 × 1011 Nm-2.)
Answer» Given: Steel cable’s length, I = 9.1 m Radius, r = 5mm = 5 × 10^-3 m. Tension in cable, F = 800 N Young’s modulus = 2 × 10¹¹ N/m² Young’s modulus, Y = \(\frac{F}{A}\) × \(\frac{l}{∆l}\) Or ∆l = \(\frac{F}{πr^2}\) × \(\frac{l}{Y}\) = \(\frac{800×9.1}{3.14×(5×10^{−3})^2×2×10^{11}}\) = 4.64 × 10^-4 m

A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is 800 N. How much has the cable stretched? (Young’s modulus for steel is 2 × 1011 Nm-2.)

Answer»

Given:

Steel cable’s length, I = 9.1 m

Radius, r = 5mm = 5 × 10^-3 m.

Tension in cable, F = 800 N

Young’s modulus = 2 × 10¹¹ N/m²

Young’s modulus,

Y = \(\frac{F}{A}\) × \(\frac{l}{∆l}\)

Or ∆l = \(\frac{F}{πr^2}\) × \(\frac{l}{Y}\)

= \(\frac{800×9.1}{3.14×(5×10^{−3})^2×2×10^{11}}\)

= 4.64 × 10^-4 m