Reply
Sat 10 Jun, 2006 07:27 pm
Ball A of mass 2 kg is moving at a velocity of 5 m/s. Ball A collides with stationary ball B also a mass of 2 kg, After the collision, ball A moves off in the direction 30 degrees to the left of its original direction. Ball B moves 60 degrees to the right of ball A's original direction, What is the velocity of each ball afer the collision?
Separate the resulting velocities into orthogonal components (one component parallel to the original direction of ball A). Preserve momentum (mv) and energy (.5mv^2). Hint: the components that are perpendicular to the original direction will have to cancel each other.
Actually, this can be solved without consideration of energy. Balancing the x and y components of momentum is sufficient to solve for the two velocities.
Momentum is the way to go, as some kinetic energy may have been lost. It could have converted into sound or heat during the collision.
If energy is lost, won't that affect momentum?
markr wrote:If energy is lost, won't that affect momentum?
This class of problems can be solved entirely by separating the velocity into orthogonal components and applying momentum conservation.
markr wrote:If energy is lost, won't that affect momentum?
Not necessarily. Inelastic collisions preserve momentum, but result in a loss of (mechanical) energy. The question doesn't specify whether this is an elastic collision or not, so it's prudent not to make assumptions about energy conservation if you don't have to.
markr wrote:If energy is lost, won't that affect momentum?
No. Momentum in a system is conserved, just as energy in a system is conserved.
2 kg (5 m/s) = 2 kg (v1)(cos 30) + 2 kg (v2)(cos 60) <----- axis of original motion
and
2 kg (v1)(sin 30) = 2 kg (v2)(sin 60) <----- axis perpendicular to original motion
Now solve for v1 and v2.
2 equations in 2 unknowns.
Stumble It!
Tweet This
Bookmark on Delicious
Share on Facebook
Share on MySpace