A merry-go-round (pictured) is sitting in a playground. It is free to rotate, but is currently stationary. You can model it as a uniform disk of mass 210 kg and radius 110 cm (consider the metal poles to have a negligible mass compared to the merry-go-round). The poles near the edge are 100 cm from the center.
Someone hits one of the poles with a 9 kg sledgehammer moving at 17 m/s in a direction tangent to the edge of the merry-go-round. The hammer is not moving after it hits the merry-go-round.
How much energy |ΔE| is lost in this collision? (enter a positive number for the absolute value in Joules)
|ΔE|=
3,42 joules
To determine the amount of energy lost in this collision, we need to calculate the change in kinetic energy. Here are the steps to do so:
1. Calculate the initial kinetic energy of the hammer before the collision. The formula for kinetic energy is given by: KE = (1/2) * mass * velocity^2. Substituting the values, we get KE_initial = (1/2) * 9 kg * (17 m/s)^2.
2. Calculate the final kinetic energy of the hammer after the collision. Since the hammer is not moving after the collision, the final kinetic energy is zero, KE_final = 0.
3. Calculate the change in kinetic energy (ΔKE). It is the difference between the initial and final kinetic energies, ΔKE = KE_final - KE_initial.
4. Take the absolute value of ΔKE to get the energy lost in the collision, |ΔE| = |ΔKE|.
Let's plug in the values and calculate:
KE_initial = (1/2) * 9 kg * (17 m/s)^2
= 1377.75 J (rounded to the nearest hundredth)
KE_final = 0 J
ΔKE = KE_final - KE_initial
= 0 J - 1377.75 J
= -1377.75 J
|ΔE| = |ΔKE|
= |-1377.75 J|
= 1377.75 J
Therefore, the amount of energy lost in this collision is 1377.75 J.