An athlete whirls a 7.40 kg hammer tied to the end of a 1.1 m chain in a horizontal circle. The hammer moves at the rate of 1.4 rev/s. What is the centripetal acceleration of the hammer? What is the tension in the chain?
Test
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
To find the tension in the chain, we can use the formula for centripetal force:
Fc = m * ac
Where:
Fc is the centripetal force
m is the mass of the hammer
ac is the centripetal acceleration
Let's calculate the centripetal acceleration first:
Step 1: Convert the given angular velocity to linear velocity
The linear velocity (v) is given by the equation v = ω * r, where ω is the angular velocity and r is the radius. Here, ω = 1.4 rev/s and r = 1.1 m.
v = 1.4 rev/s * 2π rad/rev * 1.1 m = 9.768 m/s
Step 2: Calculate the centripetal acceleration using the formula ac = (v^2) / r, where v = 9.768 m/s and r = 1.1 m.
ac = (9.768 m/s)^2 / 1.1 m ≈ 87.09 m/s^2
Now, let's calculate the tension in the chain using the centripetal force formula:
Step 3: Calculate the centripetal force using the formula Fc = m * ac, where m = 7.40 kg and ac = 87.09 m/s^2.
Fc = 7.40 kg * 87.09 m/s^2 ≈ 644.04 N
Therefore, the centripetal acceleration of the hammer is approximately 87.09 m/s^2, and the tension in the chain is approximately 644.04 N.