An Olympic hammer thrower swings a mass of 7.26 kg at the end of a light inextensible wire in a circular motion. In the final complete swing, the hammer moves at a constant speed and takes 0.8 s to complete a circle of radius 2.0 m. (i) What is the angular velocity of the hammer during its final swing? (ii) Even though the hammer moves at a constant speed, it accelerates. Explain. Calculate (iii) the acceleration of the hammer during its final swing (iv) the kinetic energy of the hammer as it is released.

Leaving Cert Physics Speed & Velocity: An Olympic hammer thrower swings

An Olympic hammer thrower swings a mass of 7.26 kg at the end of a light inextensible wire in a circular motion - Leaving Cert Physics - Question 12 - 2012

Question 12

An Olympic hammer thrower swings a mass of 7.26 kg at the end of a light inextensible wire in a circular motion. In the final complete swing, the hammer moves at a c... show full transcript

Worked Solution & Example Answer:An Olympic hammer thrower swings a mass of 7.26 kg at the end of a light inextensible wire in a circular motion - Leaving Cert Physics - Question 12 - 2012

Step 1

What is the angular velocity of the hammer during its final swing?

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Answer

To calculate the angular velocity \( \omega \), we use the formula:

\\omega = \frac{2\pi}{T} \\\

where, T is the time taken to complete one full circle. Given that it takes 0.8 seconds:

\omega = \frac{2\pi}{0.8} \approx 7.85 \text{ rad/s}

Step 2

Even though the hammer moves at a constant speed, it accelerates. Explain.

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Answer

Even though the hammer moves at a constant speed, it is undergoing circular motion. This means that the direction of the velocity vector is continuously changing even though its magnitude remains constant. Because acceleration is defined as the rate of change of velocity, and since the direction is changing, there is a centripetal acceleration directed towards the center of the circular path.

Step 3

the acceleration of the hammer during its final swing

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The centripetal acceleration ( ac) can be calculated using the formula:

a_c = \frac{v^2}{r} \\,$$ Given that the velocity (v) can be calculated from the angular velocity:

v = \omega r

Substituting the known values:

v = (7.85)(2.0) \approx 15.7 \text{ m/s}

Now substituting v into the centripetal acceleration equation:

a_c = \frac{(15.7)^2}{2.0} \approx 123.37 \text{ m/s}^2

The direction is towards the center of the orbit.

Step 4

the kinetic energy of the hammer as it is released.

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Answer

The kinetic energy (KE) of the hammer can be calculated using the formula:

KE = \frac{1}{2}mv^2

Substituting the mass and calculated velocity:

KE = \frac{1}{2}(7.26)(15.7^2) \approx 896 \\text{ J}

An Olympic hammer thrower swings a mass of 7.26 kg at the end of a light inextensible wire in a circular motion - Leaving Cert Physics - Question 12 - 2012

Worked Solution & Example Answer:An Olympic hammer thrower swings a mass of 7.26 kg at the end of a light inextensible wire in a circular motion - Leaving Cert Physics - Question 12 - 2012

What is the angular velocity of the hammer during its final swing?

Even though the hammer moves at a constant speed, it accelerates. Explain.

the acceleration of the hammer during its final swing

the kinetic energy of the hammer as it is released.

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