Q5.8 Two spheres colliding (S)
Two titanium spheres approach each other head-on with the same speed and collide elastically. After the collision, one of the spheres, whose mass is 300 g remains at rest.- What is the mass of the other sphere?
- Find the speed of the two-sphere center of mass both before and after the collision, if the initial speed of each sphere was 2 ms-1. Check each explicitly.
Solution
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Solution
Let’s draw a diagram and introduce some notation
Let the two spheres have masses and m1 and m2 respectively. The initial velocities of particles 1 and 2 are v and -v; after the collision they are 0 and v2.
To calculate the mass of the other sphere, let’s write down equations for conservation of energy and momentum:
Momentum:
m1v-m2v=m2v2Kinetic energy:
We can easily solve these two equations to get
m2=m1/3=100 g;The speed of the center of mass is a constant, since there is no external force acting on the system. We can calculate it any way we choose.
Using Key Point 4.2 before the collision
Using Key Point 4.2 after the collision