A ball of mass "m" moving with velocity "v-initial" strikes a vertical wall. The angle between the ball's initial velocity vector and the wall is "theta-initial", which depicts the situation as seen from above. The duration of the collision between the ball and the wall is "delta-t", and this collision is completely elastic. Friction is negligible, so the ball does not start spinning. In this idealized collision, the force exerted on the ball by the wall is parallel to the x axis.
What is the final angle "theta-final" that the ball's velocity vector makes with the negative y axis? Express your answer in terms of quantities given in the problem introduction.
2006-11-04 06:29:10 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Physics
Unless I'm missing something, this is a simple reflection problem, and the question is mostly about getting the axes right. Since we're seeing it "from above", gravity is not a factor, and m, delta-t and v-initial don't enter into it. Since the reaction force is parallel to the x axis, the wall runs parallel to the y axis. Assuming that theta-initial is defined relative to the plus-y axis, theta-final = -theta-initial. (That is, if theta-initial is CCW from +y, theta-final is CW from -y.)
EDIT: It seems odd that other answers are talking about conservation of momentum. It's true the y component is conserved, but momentum is a vector. The way it's conserved here is that the ball's momentum changes by m*2*v*sin(theta) along the x axis, and the momentum of the rest of the system (wall and earth) changes an equal amount in the opposite direction (resulting in an infinitesimal velocity change). If the earth were much less massive, momentum would still be conserved, but the earth would bounce away significantly and you wouldn't get a reflection like this. What's working here is conservation of energy, with infinitesimal energy lost to the earth.
2006-11-04 06:48:10 · answer #1 · answered by kirchwey 7 · 0⤊ 1⤋
Break the velocity into the x and y components and use the conservation of moment for the two x and y components. The incident angle should be equal to the reflexion angle.
2006-11-04 07:15:19 · answer #2 · answered by Dr. J. 6 · 0⤊ 2⤋
Conservation energy and momentum
2006-11-04 06:42:11 · answer #3 · answered by J 6 · 0⤊ 2⤋
Conservation of energy and momentum
2006-11-04 06:33:43 · answer #4 · answered by arbiter007 6 · 0⤊ 2⤋
theta-initial
2013-10-16 13:02:07 · answer #5 · answered by Rich 1 · 0⤊ 2⤋