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
what is the tension?

To find the centripetal acceleration of the hammer, we can use the formula:

centripetal acceleration = (angular velocity)^2 x radius

Given that the hammer moves at a rate of 1.51 rev/s, we can convert this to angular velocity in radians per second:

angular velocity = (1.51 rev/s) x (2π radians/1 rev) = 9.50 radians/s

The radius of the circular path is given as the length of the chain plus the athlete's arm length, which is 1.5 m. Therefore, the radius is also 1.5 m.

Now, we can calculate the centripetal acceleration:

centripetal acceleration = (9.50 radians/s)^2 x 1.5 m
= 90.25 m^2/s^2

So, the centripetal acceleration of the hammer is 90.25 m/s^2.

To find the tension in the chain, we can use Newton's second law of motion:

Tension = mass x (centripetal acceleration + gravitational acceleration)

The mass of the hammer is given as 7.54 kg, and the gravitational acceleration is approximately 9.8 m/s^2.

Tension = 7.54 kg x (90.25 m/s^2 + 9.8 m/s^2)
= 7.54 kg x 100.05 m/s^2
= 754.357 kg⋅m/s^2

So, the tension in the chain is approximately 754.36 N (newtons).