In the hammer throw, an athlete spins a heavy mass in a circle at the end of a c

Question

In the hammer throw, an athlete spins a heavy mass in a circle at the end of a cable before releasing it for distance as shown in (Figure 1) . For male athletes, the "hammer" is a mass of 7.3 kg at the end of a 1.2 m cable, which is typically a 3.0-mm-diameter steel cable. A world-class thrower can get the hammer up to a speed of 29 m/s. If an athlete swings the mass in a horizontal circle centered on the handle he uses to hold the cable

A) What is the tension in the cable? Neglect the gravity.

B) How much does the cable stretch? Young modulus for steel is 20×1010N/m2.

Explanation / Answer

A) tension in the cable=centripetal force on the heavy mass

=mass*speed^2/radius

=7.3*29^2/1.2

=5116.1 N

hence tension in the cable is 5116.1 N

part B:

as we know, force=young's modulous*area*change in length/length

area of the cable=pi*0.25*dimater^2=pi*0.25*(0.003)^2=7.0686*10^(-6) m^2

then

==>5116.1=20*10^10*7.0686*10^(-6)*change in length/1.2

==>change in length=5116.1*1.2/(20*10^10*7.0686*10^(-6))=4.3427 mm

hence the cable is stretched by 4.3427 mm

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