Pulse

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Impact processes in which the bodies separate again

The total momentum is the vector sum of the momentum of all bodies involved in the impact. The speeds before the collision are here with $v_{i}$ and after the shock with $u_{i}$ designated.

Total momentum before the collision:

p_{ges, before} = m_{1} \cdot v_{1} + m_{2} \cdot v_{2} + ...

Total momentum after the collision:

p_{ges, afterwards} = m_{1} \cdot u_{1} + m_{2} \cdot u_{2} + ...

Measurement: shock in which the bodies separate again

Use the measurement tables to calculate the mean value of the momentum of both bodies before and after the impact. Calculate separately for the x and y components. Compare the total momentum in the x and y directions before and after the collision. Interpret the result.

Note: The shock takes place approximately at the time $t = 0,4 s$ instead of. You should therefore not use this measured value as well. The mass of the left puck is $210 G$ that of the right $240 G$ .

Tab. 1

Left puck	Right puck
$t$ [ $s$ ]	$v_{x}$ [ $m s^{-1}$ ]	$v_{y}$ [ $m s^{-1}$ ]	$v_{x}$ [ $m s^{-1}$ ]	$v_{y}$ [ $m s^{-1}$ ]
0,0	0,67	0,00	0,00	0,38
0,1	0,67	0,00	-0,05	0,38
0,2	0,72	0,05	-0,05	0,38
0,4	0,57	-0,14	0,14	0,38
0,6	0,19	-0,19	0,48	0,57
0,8	0,19	-0,14	0,43	0,53
0,10	0,19	-0,14	0,48	0,53

Result:

Left puck, impulse before the shot:

\begin{array}{l} p_{x, l} = m_{l} \cdot v_{x, l} \approx 0,14 kg m s^{-1} \\ p_{y, l} = m_{l} \cdot v_{y, l} \approx 0,00 kg m s^{-1} \end{array}

Right puck, impulse before the shot:

\begin{array}{l} p_{x, r} = m_{r} \cdot v_{x, r} \approx - 0 ,01 kg m s^{-1} \\ p_{y, r} = m_{r} \cdot v_{y, r} \approx 0,10 kg m s^{-1} \end{array}

Total momentum before the collision:

\begin{array}{l} p_{x} = p_{x, l} + p_{x, r} \approx 0,15 kg m s^{-1} \\ p_{y} = p_{y, l} + p_{y, r} \approx 0,10 kg m s^{-1} \end{array}

Left puck, impulse after the shot:

\begin{array}{l} p_{x, l} = m_{l} \cdot v_{x, l} \approx 0,04 kg m s^{-1} \\ p_{y, l} = m_{l} \cdot v_{y, l} \approx -0,03 kg m s^{-1} \end{array}

Right puck, impulse after the shot:

\begin{array}{l} p_{x, r} = m_{r} \cdot v_{x, r} \approx 0,11 kg m s^{-1} \\ p_{y, r} = m_{r} \cdot v_{y, r} \approx 0,13 kg m s^{-1} \end{array}

Total momentum after the collision:

\begin{array}{l} p_{x} = p_{x, l} + p_{x, r} \approx 0,15 kg m s^{-1} \\ p_{y} = p_{y, l} + p_{y, r} \approx 0,10 kg m s^{-1} \end{array}

It can be seen that the x-component of the total impulse before and after the collision is equal within the scope of the measurement accuracy, as is the y-component. It follows that the magnitude and direction of the total momentum before and after the collision are the same.