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. 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 20×10^10 N/m^2.

Answer 1

In the hammer throw, the 1.2 m steel cable holding a 7.3 kg mass experiences a tension of 502.35 N, resulting in a stretch of approximately 0.449 mm when the hammer is spun at 29 m/s.

To address the student's question about the hammer throw, we'll need to use circular motion equations and material properties.

a) The tension in the cable is the centripetal force required to keep the hammer moving in a circle at a constant speed. This can be calculated using the equation Fc = m∙v2/r. Given a 7.3 kg mass, a velocity of 29 m/s, and a radius of 1.2 m, we find that the tension is 502.35 N.

b) The amount the cable stretches can be found using Hooke's Law and the definition of Young's modulus (Y = stress/strain), along with the original length and cross-sectional area of the cable. Assuming a cylindrical shape, the calculation reveals a stretch of 0.000449 m or 0.449 mm.

So, when a world-class athlete throws the hammer at a speed of 29 m/s, the tension in the 1.2 m cable is 502.35 N, and this tension leads to the steel cable stretching by approximately 0.449 mm.

Answer 2

a) The tension in the cable is approximately 5044.75 Newtons (N).

b) The cable stretches approximately 4 centimeters (0.04 meters or 40 millimeters) when the hammer is swung in a horizontal circle.