Center of mass and velocity problem

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To find the velocity of the center of mass for two particles, one with a mass of 5.30 kg moving east at 10.0 m/s and another with a mass of 18.0 kg moving west at 10.0 m/s, the correct formula is Vcm = P/M. The total momentum P is calculated using the correct masses and velocities, leading to Vcm = [(5.30 kg)(10 m/s) + (18.0 kg)(-10 m/s)] / (5.30 kg + 18.0 kg). The negative sign for the westward velocity is crucial for accurate calculations. The resulting velocity of the center of mass is not 10 m/s, highlighting the importance of using the correct values and signs in the equation.
kbyws37
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If a particle of mass 5.30 kg is moving east at 10.0 m/s and a particle of mass 18.0 kg is moving west at 10.0 m/s, what is the velocity of the center of mass of the pair?


I used the equation
Vcm = P/M
Vcm = [(5.70)(10) + (15)(10)] / [(5.70)+(15)]
Vcm = 10 ms

however, it says that is not the correct answer.
I don't understand why. can someone help?
thanks
 
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kbyws37 said:
If a particle of mass 5.30 kg is moving east at 10.0 m/s and a particle of mass 18.0 kg is moving west at 10.0 m/s, what is the velocity of the center of mass of the pair?


I used the equation
Vcm = P/M
Vcm = [(5.70)(10) + (15)(10)] / [(5.70)+(15)]
Vcm = 10 ms

however, it says that is not the correct answer.
I don't understand why. can someone help?
thanks
Re-write your equation with units. Does everything work out? Are you putting the right numbers in the right places? It's hard to tell without units. Are all your signs correct?
 
Vcm = P/M where P is (mass kg)(velocity m/s) and where M is the total mass (kg)

Vcm = [(5.70kg)(10m/s) + (15kg)(10m/s)] / [(5.70kg)+(15kg)]
Vcm = 10 m/s

I'm still getting it wrong.
 
You seem to have put 5.7 kg instead of 5.3 kg and 15 kg instead of 18 kg.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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