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 200 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 97 cm from the center.

Question

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 200 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 97 cm from the center.

Someone hits one of the poles with a 9 kg sledgehammer moving at 19 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 is lost in this collision? (enter a positive number for the absolute value in Joules)

Answer 1

help plase

Answer 2

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.

Answer 3

so the radius is not important???

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

v_1'=mhammer*vhammer/Mmerry???!!!!

Answer 4

To determine the amount of energy lost in the collision, we need to calculate the change in kinetic energy before and after the collision.

First, let's calculate the initial kinetic energy of the sledgehammer. The formula for kinetic energy is:

K = (1/2) * m * v^2

Where:
K is the kinetic energy
m is the mass of the sledgehammer (9 kg)
v is the initial velocity of the sledgehammer (19 m/s)

Plugging in the values, we get:
K_initial = (1/2) * 9 kg * (19 m/s)^2
= 1714.5 J (rounded to one decimal place)

Now, let's calculate the final kinetic energy of the sledgehammer. Since it comes to rest after the collision, the final kinetic energy is 0 J.

To find the energy lost in the collision, we can subtract the final kinetic energy from the initial kinetic energy:
Energy lost = K_initial - K_final
= 1714.5 J - 0 J
= 1714.5 J

Therefore, the amount of energy lost in this collision is 1714.5 joules.