An athlete whirls a 7.36 kg hammer tied to
the end of a 1.5 m chain in a horizontal circle.
The hammer moves at the rate of 1.07 rev/s.
What is the centripetal acceleration of the
hammer? Assume his arm length is included
in the length given for the chain.
What is the tension in the chain?
acceleration=w^2*radius
w=1.07*2PI radians/sec
To find the centripetal acceleration of the hammer, we can use the formula:
\(a = \frac{{v^2}}{{r}}\)
Where:
- \(a\) is the centripetal acceleration
- \(v\) is the velocity of the hammer
- \(r\) is the radius of the circular motion
Given:
- Mass of the hammer (\(m\)) = 7.36 kg
- Length of the chain including the athlete's arm (\(L\)) = 1.5 m
- Rate of revolution (\(f\)) = 1.07 rev/s
First, we need to find the velocity (\(v\)) of the hammer. We know that the rate of revolution is given in rev/s, so we need to convert it to radians per second (rad/s).
To convert revolutions to radians, we can use the conversion:
\(2\pi \text{ radians} = 1 \text{ revolution}\)
So, \(f\) rev/s will be \(f \times 2\pi\) rad/s.
Let's calculate the velocity of the hammer:
\(v = f \times 2\pi \times r\)
Next, we need to find the radius (\(r\)) of the circular motion. Since the length of the chain \(L\) includes the athlete's arm, the radius will be \(L - \text{length of the athlete's arm}\).
Now that we have the velocity and the radius, we can calculate the centripetal acceleration using the formula mentioned earlier:
\(a = \frac{{v^2}}{{r}}\)
To find the tension in the chain, we can use the following equation:
\(T = m \times a\)
Where:
- \(T\) is the tension in the chain
- \(m\) is the mass of the hammer
- \(a\) is the centripetal acceleration
Let's plug the given values into the formulas and solve for the centripetal acceleration and the tension.