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 190 kg and radius 100 cm (consider the metal poles to have a negligible mass compared to the merry-go-round). The poles near the edge are 90 cm from the center.

Someone hits one of the poles with a 8 kg sledgehammer moving at 18 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 (modulus of (deltaE)) is lost in this collision? (enter a positive number for the absolute value in Joules)

example of inelastic collision, where momentum before = momentum after, and simply calculate the difference in energy then!

hi enjoy, what is the use of radius here?

1/2 *[(m_1*m_2)/m_1+m_2)]*v_1^2

So Anonymous you got 964.29 N??

First, get all the variables:

m_1: The mass of the merry-go-round
m_2: The mass of the sledgehammer
v_1: The velocity of the merry-go-round before the collision
v_2: The velocity of the sledgehammer before the collision
v_1': The velocity of the merry-go-round after the collision
v_2': The velocity of the sledgehammer after the collision

Apply the conservation of momentum:

(m_1*v_1)+(m_2*v_2)=(m_1*v_1')+(m_2*v_2')

You know everything except for v_1', so you can solve the above equation for v_1'. Then look at the difference in kinetic energy before and after the collision:

((0.5*m_1*v_1^2)+(0.5*m_2*v_2^2))-((0.5*m_1*v_1'^2)+(0.5*m_2*v_2'^2))

The above is your answer.

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so the radius is not important???

and we'll have to consider v_1=0 and v_2'=0

To find the amount of energy lost in this collision, we can use the principle of conservation of linear momentum and kinetic energy.

First, let's calculate the initial linear momentum of the sledgehammer:

Linear momentum (p) = mass (m) * velocity (v)
p_initial = 8 kg * 18 m/s = 144 kg*m/s

When the sledgehammer hits the merry-go-round, the system (sledgehammer + merry-go-round) is at rest. After the collision, both the sledgehammer and the merry-go-round start moving together.

To calculate the final velocity of the system (vf), we can use the conservation of linear momentum:

p_initial = p_final
144 kg*m/s = (mass of the system) * vf

The mass of the system is the sum of the mass of the sledgehammer and the mass of the merry-go-round:

mass system = 8 kg + 190 kg = 198 kg

Now, let's find vf:

vf = 144 kg*m/s / 198 kg = 0.727 m/s

Now that we have the final velocity of the system, we can calculate the final kinetic energy of the system (KE_final):

KE_final = 0.5 * mass system * (vf)^2
KE_final = 0.5 * 198 kg * (0.727 m/s)^2
KE_final = 64.23 J

The initial kinetic energy of the sledgehammer can be calculated using:

KE_initial = 0.5 * mass sledgehammer * (velocity)^2
KE_initial = 0.5 * 8 kg * (18 m/s)^2
KE_initial = 1296 J

The energy lost in this collision is given by the difference between the initial kinetic energy and the final kinetic energy:

deltaE = KE_initial - KE_final
deltaE = 1296 J - 64.23 J
deltaE ≈ 1231.77 J

Therefore, the energy lost in this collision is approximately 1231.77 Joules.

First Calculate the KE of the sledge hammer.

2: Calculate the speed of the Merry-go-round (MGR) from m1.v1+m2.v2=m1.v1'+m2.v2'. Note: v2 and v1' are zero
3: Calculate angular KE of the MGR
4: Lost energy =1-3

So if you can't solve this then you should go to elementary school