How Do You Calculate the Velocity of the Center of Mass?

AI Thread Summary
To calculate the velocity of the center of mass (vcm) for two blocks moving along the x-axis, use the formula vcm = [(m1)(v1x) + (m2)(v2x)] / (m1 + m2). This equation incorporates the masses (m1, m2) and their respective velocities (v1x, v2x). If the masses are unknown, the problem can be challenging, but the concept remains that vcm is a weighted average of the individual velocities based on their masses. The discussion emphasizes the importance of understanding the relationship between position, mass, and velocity in calculating the center of mass. Overall, the formula provides a clear method for determining vcm when the necessary variables are available.
akaur
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1. Recall that the blocks can only move along the x axis. The x components of their velocities at a certain moment are v1x and v2x. Find the x component of the velocity of the center of mass (vcm)x at that moment. Express your answer in terms of m1, m2, v1x, and v2x



2. Keep in mind that, in general: v= dx/dt.



3. its the derivative of xcm = (m1x1 + m2x2) / (m1 + m2)...so does vcm= [(m1)(v1x) + (m2)(v2x)] / (m1 + m2) ?
 
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akaur said:
1. Recall that the blocks can only move along the x axis. The x components of their velocities at a certain moment are v1x and v2x. Find the x component of the velocity of the center of mass (vcm)x at that moment. Express your answer in terms of m1, m2, v1x, and v2x



2. Keep in mind that, in general: v= dx/dt.



3. its the derivative of xcm = (m1x1 + m2x2) / (m1 + m2)...so does vcm= [(m1)(v1x) + (m2)(v2x)] / (m1 + m2) ?


yes. looks right to me.
 
what if you don't have the masses, cause I am stuck on one question that has just 2 velocities going in the positive x direction
 

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