SPH OA Collisions in Two Dimensions Investigation
Problem:
Is momentum conserved in a two-dimensional collision?
Materials:
2 steel balls (ball bearings) 1 glass ball (marble) carbon paper
masking tape paper C-clamp
2-D collision apparatus (set up as in diagram)
Procedure:
1. Swivel the target support around until it is lined up with the curved ramp. Place a steel ball on the target support and adjust the distance to the end of the ramp so that the support is two radii (2R) from it (see illustration).
2.
Remove the steel ball from the target support and place it on the ramp exactly 25 cm from the end. Release it from this point. It should just clear the support. If a small click is heard, the ball is touching the support as it is launched. Adjust the height of the target support to prevent this.
3. Place carbon paper on the floor, black side up. Cover it completely with a large piece of tracing paper or newsprint. Position the paper so that the plumb line, suspended from the target support, hangs over the middle of one end of the paper, approximately 10 cm from a corner. Tape the paper to the floor. Mark the point directly beneath the plumb bob with an X.
4. Determine the initial horizontal momentum of the incident ball before the collision, by releasing it about 10 times. Circle the distribution of "landings" on the paper. Using a ruler, draw a vector from the point X to the centre of the distribution of points. This vector represents the initial momentum of the incident ball (see marginal note).
5. Place an identical steel ball on the target support. Swivel the support sideways about 45° to produce an off-centre collision between the incident and the target balls. Record the point of collision, Xv directly below the plumb bob. The incident ball is released from the 25 cm mark on the ramp. The two balls should hit the paper at two different points. Mark both impact points 1.
6. Swivel the target ball to different positions and repeat step 5", for at least four more collisions. Label the pairs of impact points 2, 3, 4, etc., and the corresponding points of collision X2,X3,X4,....
7. To draw the vectors representing the momenta after collision, join the point Xn to the impact points for both the incident ball and the target ball for the Xn collision.
8. Add the two momentum vectors graphically (on the paper) for each collision, placing the tail of the momentum vector for the target ball at the head of the momentum vector for the incident ball. Compare this vector sum with both the magnitude and the direction of the momentum vector of the incident ball before the collision (step 4). For each collision determine whether momentum is conserved (in a two-dimensional collision).
9. Repeat the investigation, using the same incident steel ball but a lighter target glass ball of the same diameter. Using a new sheet of tracing paper, record the incident velocity of the steel ball (see step 4). Next, place the glass target ball on the target support and record at least four off-centre collisions. Finally, draw in the velocity vectors for each collision.
10. Check to see whether the vector sum of the velocity vectors of both balls after the collision is equal to the velocity vector of the incident steel ball. Discuss.
11. Using a balance, determine the masses of the steel ball and the glass ball. What is the ratio of the mass of the glass ball to that of the steel ball?
12. Convert the velocity vectors in the collision to momentum vectors, using the mass ratio calculated in step 11 (see notes below). Is momentum conserved when unequal masses collide?
Notes:
· momentum is mass x velocity
· after a collision, the mass alters the length of the velocity vector but not the direction
· if the mass of the steel ball is considered to be 1, then its velocity vector also represents the momentum vector ie.
· but the velocity vector for the glass ball must be reduced to properly represent the momentum vector (since glass has less mass than steel)
· length of the momentum vector of the glass ball is calculated from:
http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/Collision/jarapplet.html
http://ww2.unime.it/dipart/i_fismed/wbt/mirror/ExplrSci/dswmedia/2dcollis.htm
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