Question

A mine elevator cage with a mass of 2.5 tons empty is descending at a rate of 32 km/hr when the hoist mechanism jams and stops suddenly. If the cable is steel with a cross-sectional area of 6.5 cm2 and the cage is 1500 meters below the hoisting drum when the drum jams, which of the following most nearly equals the stress in the cable? (E for hoist cable equals 84,000 x 106 Pa, neglect the weight of the cable)

Answer 1

Answer:

σ = 4.1 MPa

Explanation:

Given that

m= 2.5 kg

v=  32 km.hr

v= 8.88 m/s

The kinetic energy of the mass ,KE

KE = mv²/2

KE = 2.5 x 8.88²/2

KE= 98.56 J    -------1

The strain energy of the string

$E=\dfrac{\sigma^2}{2E}AL$

$E=\dfrac{\sigma^2}{2\times 84,000\times 10^6}\times 6.5\times 10^{-4}\times 1500$

$E={\sigma^2}\times {5.80\times 10^{-12}}$ ----2

KE= E

$98.56={\sigma^2}\times {5.80\times 10^{-12}}$

$\sigma =\sqrt{\dfrac{98.56}{5.80\times 10^{-12}}}$

σ = 4.1 MPa