Conservation of Momentum in Collisions

Name:

Lab Partners:

When entering numeric data, use exponentials: ie., 1.6 * 10^-19 = 1.6E-19.

Procedure

1. Assemble the air table and CAREFULLY level it. Measure the masses of the pucks:

   m1 = g

   m2 = g

2. Under guidance from the instructor, obtain a spark record of a collision of the two pucks. The pucks should be gently but firmly set in motion with differing angles of approach and initial speeds, and the collision should be direct as opposed to glancing. Exercise extreme caution with the apparatus: the spark generator can generate voltages in excess of 30,000 volts!
3. Identify the sparks closest to the collision for each of the four tracks (before and after the collision, for each puck). Measure the distance for 10 time intervals away from the collision for each track:

   d1, b = cm				d2, b = cm
   d1, a = cm				d2, a = cm

4. Choose a convenient orientation for the x and y axes and measure the angle of each track with the x axis:

   q1, b = degrees				q2, b = degrees
   q1, a = degrees				q2, a = degrees

Analysis

1. Assuming that the sparks occurred at intervals of 1/50 s, compute the speeds of each puck before and after the collision:

   v_{i, j} = d_{i, j} / (10 / 50)

   v1, b = cm / s				v2, b = cm / s
   v1, a = cm / s				v2, a = cm / s

2. Compute the x and y components of all four momentum vectors. Take care that the signs are correct (typically all y components will be positive because all tracks are plotted as moving from negative y to positive y, but x components of tracks moving left should be negative!):

   p_{i, j, x} = m_i v_{i, j} Cos ( q_{i, j} )

   p_{i, j, y} = m_i v_{i, j} Sin ( q_{i, j} )

   p1, b, x = g cm / s				p2, b, x = g cm / s
   p1, b, y = g cm / s				p2, b, y = g cm / s
   p1, a, x = g cm / s				p2, a, x = g cm / s
   p1, a, y = g cm / s				p2, a, y = g cm / s

3. Compute the net gain and the relative errors between the x components of 1) the sum of the approach vectors and 2) the sum of the retreat vectors. Use the average of the absolute values of the approach vector components in the denominator for the relative error computation. This means that the error is relative to the magnitude of the momentum and not to the sum (which may be very small!).

   p_{x, net} = p_{1, a, x} + p_{2, a, x} - ( p_{1, b, x} + p_{2, b, x} ).

   p_{x, rel} = 100 % x | p_{x, net} | / ( ( | p_{1, b, x} | + | p_{2, b, x} | ) / 2 ).

   Repeat for the y components:

   px, net = g cm / s				py, net = g cm / s
   px, rel = %				py, rel = %

   What can you conclude?