An athlete whirls a 7.54 kg hammer tied to the end of a 1.5 m chain in a horizontal circle.
The hammer moves at the rate of 1.51 rev/s.
What is the centripetal acceleration of the
hammer? Assume his arm length is included in the length given for the chain.
Answer in units of m/s2
To find the centripetal acceleration of the hammer, we can use the formula:
a = (v^2) / r
where
a is the centripetal acceleration,
v is the tangential velocity of the hammer, and
r is the radius of the circular path.
In this case, the tangential velocity can be determined by multiplying the velocity in revolutions per second (rev/s) by the circumference of the circle:
v = (2πr) * (1.51 rev/s)
Given that the length of the chain is 1.5 m, we can determine the radius of the circular path by subtracting the length of the athlete's arm:
r = 1.5 m - arm length
Now we can substitute these values back into the formula to find the centripetal acceleration:
a = ((2πr) * (1.51 rev/s))^2 / r
Finally, we can simplify and calculate the result.