Answer and Explanation:
To find the kinetic energy (KE) of the wrecking ball at the bottom of its swing, we can use the conservation of mechanical energy principle. The total mechanical energy of the wrecking ball remains constant throughout its motion, meaning the sum of its potential energy and kinetic energy remains the same.
1. Calculate the potential energy (PE) at the top of the swing:
PE = mgh
where m is the mass of the wrecking ball (125 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the swing.
In this case, the height is the length of the cable (15.4 m). So,
PE = 125 kg * 9.8 m/s^2 * 15.4 m
2. Calculate the kinetic energy (KE) at the bottom of the swing:
At the bottom of the swing, all of the potential energy is converted into kinetic energy. Therefore,
KE = PE
Substitute the value of PE calculated in step 1 to find KE.
Simplifying and calculating the value of PE:
PE = 125 kg * 9.8 m/s^2 * 15.4 m
Then, substitute the value of PE into KE:
KE = 125 kg * 9.8 m/s^2 * 15.4 m
Perform the multiplication to find the final answer for KE.
It's important to note that in this calculation, we assume no energy losses due to factors like air resistance or friction. Additionally, this calculation assumes that the cable is massless and the height of the swing is measured from the point of release to the bottom of the swing.