In the field event known as the hammer throw, an athlete spins a heavy mass in a circle at the end of a chain. When the athlete lets go of the chain, the mass flies off in a parabolic arc; the winner is the one who gets the maximum distance. For male athletes, the hammer is a mass of 7.30 kg at the end of a 1.20 m chain. A world-class thrower can get the hammer up to a speed of 29.0 m.s-1. If an athlete swings the mass in a horizontal circle centered on the handle he uses to hold the chain (figure 2 below), what is the tension in the chain at this maximum speed? Include the unit for tension in your answer
To determine the tension in the chain at the maximum speed, we can start by using the formula for centripetal force:
F = (mv^2) / r
Where:
F is the centripetal force
m is the mass of the hammer (7.30 kg)
v is the velocity of the hammer (29.0 m/s)
r is the radius of the circular path (1.20 m)
Plugging in the given values, we have:
F = (7.30 kg * (29.0 m/s)^2) / 1.20 m
Calculating the numerator:
(7.30 kg * (29.0 m/s)^2) = 5849.70 kg⋅m/s^2
Now, we can substitute this value and the given radius into the centripetal force formula:
F = (5849.70 kg⋅m/s^2) / 1.20 m
Simplifying:
F = 4874.75 N
Therefore, the tension in the chain at the maximum speed is 4874.75 Newtons (N).
To find the tension in the chain at the maximum speed of 29.0 m/s, we can start by analyzing the forces acting on the hammer.
In this case, the only forces acting on the hammer are the tension in the chain and the force of gravity. The force of gravity acts vertically downward with a magnitude given by the weight of the hammer:
Weight = mass x acceleration due to gravity
Weight = 7.30 kg x 9.8 m/s² (acceleration due to gravity)
Weight = 71.54 N (rounded to two decimal places)
Since the hammer is in circular motion, there must be a net centripetal force acting towards the center of the circle. This centripetal force is provided by the tension in the chain.
The centripetal force is given by the equation:
Centripetal force = mass x velocity² / radius
Here, the mass of the hammer is 7.30 kg, and the velocity is 29.0 m/s. The radius of the circular motion is given as 1.20 m.
Plugging in these values:
Centripetal force = 7.30 kg x (29.0 m/s)² / 1.20 m
Centripetal force = 5274.2 N (rounded to one decimal place)
Since the tension in the chain is equal to the centripetal force, the tension in the chain at the maximum speed is 5274.2 N.
Therefore, the tension in the chain at the maximum speed is 5274.2 N (newtons).