# Center of mass and velocity problem

• kbyws37
In summary: Double check your numbers and units and try again. Also, make sure you are using the correct signs for direction (+ for east, - for west).
kbyws37
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

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.

## 1. What is the center of mass?

The center of mass is the point at which the mass of an object is evenly distributed in all directions. It is the average location of the weight of an object.

## 2. How is the center of mass calculated?

The center of mass can be calculated by finding the weighted average of the positions of all the individual particles that make up an object. This is done by multiplying the position of each particle by its mass and then dividing the sum of these values by the total mass of the object.

## 3. Why is the center of mass important in physics?

The center of mass is important in physics because it helps us to understand the motion of objects. It is used to calculate the overall motion of an object and is essential in determining the stability and balance of objects.

## 4. What is the relationship between center of mass and velocity?

The center of mass and velocity are closely related in that the velocity of the center of mass is equal to the total momentum of the object divided by its total mass. This means that the velocity of the center of mass is a measure of the overall motion of the object.

## 5. Can the center of mass ever be outside of an object?

No, the center of mass will always be within the boundaries of an object. This is because the center of mass is dependent on the distribution of mass within the object, and if all of the mass is contained within the object, the center of mass must also be contained within it.

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