Answer:
The velocity will be v1 = 0.58[m/s]
Explanation:
This problem can be solved by the law of conservation of the moment, which explains that the moment of a system remains constant because there are no external forces acting on it.
We have the following initial data:
m1 = mass of the skater = 55 [kg]
m2 = mass of the ball = 3 [kg]
v2 = velocity of the ball = 8 [m/s]
Therefore:
![m_{1}*v_{1}+m_{2}*v_{2}=m_{1}*v_{1}+m_{2}*v_{2}\\(50*0)+(3*0)=(50*v_{1})+(3*8)\\50+3-24=50*v_{1}\\v_{1}= 0.58[m/s]](https://tex.z-dn.net/?f=m_%7B1%7D%2Av_%7B1%7D%2Bm_%7B2%7D%2Av_%7B2%7D%3Dm_%7B1%7D%2Av_%7B1%7D%2Bm_%7B2%7D%2Av_%7B2%7D%5C%5C%2850%2A0%29%2B%283%2A0%29%3D%2850%2Av_%7B1%7D%29%2B%283%2A8%29%5C%5C50%2B3-24%3D50%2Av_%7B1%7D%5C%5Cv_%7B1%7D%3D%200.58%5Bm%2Fs%5D)
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pressure absolute = pressure gage + pressure atmosphere
Answer:
r = 0.491 m
Explanation:
In this case the System is formed by the teacher with the two masses, so the forces during movement are internal and the angular momentum is conserved
Initial.
L₀ = I₀ w₀
Final
Lf = I w
L₀ = Lf
I₀ w₀ = I w
The moment of inertia is
I₀ = m r₀²
I = m r²
Let's replace
m r₀² w₀ = m r² w
r² = r₀² w₀ / w
Angular velocity
w₀ = 10 rpm (2pi rad / 1 rev) (1 min / 60 s) = 1.047 rad / s
w = 32.5 rpm = 3.403 rad / s
Let's calculate
r = √(0.785 1.047 / 3.403)
r = 0.491 m
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