An athlete whirls a 7.17 kg hammer tied to
the end of a 1.5 m chain in a horizontal circle.
The hammer moves at the rate of 1.76 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/s
2
016 (part 2 of 2) 10
To find the centripetal acceleration of the hammer, we can use the formula:
ac = (v^2) / r
where ac is the centripetal acceleration, v is the velocity of the hammer, and r is the radius of the circular path.
Given that the hammer moves at a rate of 1.76 rev/s, we need to convert this angular velocity to linear velocity. One revolution (rev) is equivalent to the circumference of the circle, which is given by:
circumference = 2 * π * r
Since the length of the chain includes the athlete's arm length of 1.5 m, the radius of the circular path can be calculated as:
r = chain length - arm length
r = 1.5 m - 1.5 m
r = 0 m
However, this means that the chain length is 1.5 m, and the hammer is moving in a vertical circle, not a horizontal circle. Therefore, let's assume that the question is referring to a different situation where the hammer is moving in a horizontal circle and the arm length is not included.
With that assumption, the radius of the circular path is 1.5 m. We are given that the hammer moves at a rate of 1.76 rev/s, so we can calculate the linear velocity (v) as:
v = (1.76 rev/s) * 2 * π * r
Substituting the value of r:
v = (1.76 rev/s) * 2 * π * 1.5 m
Now, we can plug the value of v into the centripetal acceleration formula:
ac = (v^2) / r
ac = [(1.76 rev/s) * 2 * π * 1.5 m]^2 / 1.5 m
Simplifying the expression:
ac = [(1.76 * 2 * 3.14 * 1.5 m/s) / 1.5 m]^2
ac = (9.348 m/s)^2
Finally, we can solve for the centripetal acceleration:
ac = 87.3 m/s^2
Therefore, the centripetal acceleration of the hammer is 87.3 m/s^2.