the figure below shows the top view of two balls colliding on a horizontal frictionless table. the path…
the figure below shows the top view of two balls colliding on a horizontal frictionless table. the path followed by the center of mass of this system is shown by the black vector. which path, labeled a, b, c, or d, will the center of mass follow after the collision? center of mass
Answer
Explanation:
Step1: Recall the law of conservation of momentum
In the absence of external forces (the table is frictionless, and assuming no other external forces act on the system of two balls), the momentum of the system is conserved. The velocity of the center of mass (\vec{v}{cm}=\frac{\sum{i = 1}^{n}m_{i}\vec{v}{i}}{M}), where (M=\sum{i=1}^{n}m_{i}). Since there is no external force (F_{ext}=\frac{d\vec{P}}{dt}), and (F_{ext} = 0), then (\vec{P}) (total momentum of the system) is constant. And (\vec{v}_{cm}=\frac{\vec{P}}{M}), so the velocity of the center of mass is constant.
Step2: Analyze the direction of the center - of - mass velocity
Before the collision, the center of mass has a certain velocity (given by the black vector). After the collision, because there is no external force, the direction and magnitude of the velocity of the center of mass do not change. Looking at the paths labeled A, B, C, and D, path B has the same direction as the initial velocity of the center of mass (along the (+x) direction before and after the collision, as the black vector and path B are colinear with the (+x) - axis in terms of direction)
Answer:
B