PhysicsBowl 2016 Q26

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PhysicsBowl 2016

26) This question asks us to find the speed of the center of mass of the system described. We can start with the center of mass of the system. Since all masses are moving either right or left (in 1-dimensional) we will only consider the center of mass in this component.

Where x[cm] is center of mass, m is mass, and x is position

We know we can find the velocity of an object by taking the time-derivative of the object's position equation. We can do the same with the center of mass to get the velocity of the center of mass!

Where x[cm] is center of mass, m is mass, x is position, t is time, v[cm] is velocity of center of mass, v is velocity, and p is momentum

We can now see the relationship between the velocity of the center of mass and the mass and volume of each object. We can start plugging in our given values.

Where v[cm] is velocity of center of mass, m is mass, and v is velocity

Notice that our final answer is 3.00 m/s. We don't need to mention direction because the question only asks for the speed of the center of mass.

Answer: C