An athlete whirls a 7.36 kg hammer tied to
the end of a 1.5 m chain in a horizontal circle.
The hammer moves at the rate of 1.07 rev/s.
What is the centripetal acceleration of the
hammer? Assume his arm length is included
in the length given for the chain
and What is the tension in the chain?
To find the centripetal acceleration of the hammer, we can use the formula:
centripetal acceleration = (angular velocity)^2 * radius
Where the angular velocity is given as 1.07 rev/s and the radius is the length of the chain, which is 1.5 m.
First, let's convert the angular velocity from revolutions per second to radians per second. Since there are 2π radians in one revolution, we can multiply the angular velocity by 2π to convert it:
angular velocity = 1.07 rev/s * 2π rad/rev = 6.73 rad/s
Now we can substitute the values into the centripetal acceleration formula:
centripetal acceleration = (6.73 rad/s)^2 * 1.5 m = 71.72 m/s^2
Therefore, the centripetal acceleration of the hammer is 71.72 m/s^2.
Next, let's find the tension in the chain. The tension in the chain provides the necessary centripetal force to keep the hammer moving in a circular path.
We can use the centripetal force formula:
centripetal force = mass * centripetal acceleration
The mass of the hammer is given as 7.36 kg and the centripetal acceleration is 71.72 m/s^2 (as calculated earlier).
Substituting the values into the formula:
centripetal force = 7.36 kg * 71.72 m/s^2 = 527.59 N
Therefore, the tension in the chain is 527.59 N.