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|=
You forgot to mention that this problem is part if your 8.01 MIT exam and asking for help during your exam is a violation of the Honor Code.
And why exactly are you here?
you can work omega out of conservation of momentum.
then get rotational KE using that omega.
then the energy loss should be
initial KE_hammer - rotational KE
eh eh honor code eh eh eh
*you can work omega out of conservation of momentum*
do you add the momentum of inertia of the sledgehammer to the merrygoround?
cuz when I do, I get the wrong answer.
How would I get omega from here? Please help.
that one is obvious, no?
s = r * theta
ds/dt = r dtheta/dt
v = r * omega
I still don't get it..
To calculate the energy lost in the collision, we need to first determine the initial kinetic energy of the sledgehammer and then calculate the final kinetic energy after the collision. The difference between the initial and final kinetic energies will give us the energy lost.
1. Calculate the initial kinetic energy of the sledgehammer:
The initial kinetic energy (KE_initial) is given by the formula:
KE_initial = 0.5 * mass * velocity^2
Given:
Mass of the sledgehammer (m) = 9 kg
Velocity of the sledgehammer (v) = 17 m/s
Using the formula, we can calculate:
KE_initial = 0.5 * 9 kg * (17 m/s)^2 = 1311.5 J (rounded to one decimal place)
2. Determine the final kinetic energy of the sledgehammer after the collision:
Since the sledgehammer comes to rest after the collision, its final kinetic energy (KE_final) is zero.
3. Calculate the energy lost (|ΔE|):
The energy lost in the collision (|ΔE|) is equal to the difference between the initial and final kinetic energies:
|ΔE| = KE_initial - KE_final
Substituting the values, we have:
|ΔE| = 1311.5 J - 0 J = 1311.5 J
Therefore, the energy lost in this collision is 1311.5 Joules.