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:
ac = (v^2) / r
Where:
ac is the centripetal acceleration
v is the linear velocity of the hammer
r is the radius of the circular path
In this case, the linear velocity is given in terms of revolutions per second (rev/s). To convert this to linear velocity, we need to multiply it by the circumference of the circular path. The circumference can be found using the formula:
C = 2πr
Given that the radius is 1.5 m, we can find the circumference:
C = 2π * 1.5 = 9.42 m
Now, we can find the linear velocity:
v = C * revolutions per second = 9.42 * 1.51 = 14.2292 m/s
Substituting the values into the formula for centripetal acceleration:
ac = (14.2292^2) / 1.5 = 143.1364 m/s^2
So, the centripetal acceleration of the hammer is 143.1364 m/s^2.
To find the tension in the chain, we can use the centripetal force formula:
Fc = m * ac
Where:
Fc is the centripetal force
m is the mass of the hammer
Given that the mass of the hammer is 7.54 kg, we can calculate the centripetal force:
Fc = 7.54 kg * 143.1364 m/s^2 = 1080.0103 N
So, the tension in the chain is 1080.0103 N.