9.3 Conservation of linear momentum  (Page 6/10)

Let’s define upward to be the + y -direction, perpendicular to the surface of the comet, and $y=0$ to be at the surface of the comet. Here’s what we know:

• The mass of Comet 67P: $M_c=1.0\times {10}^{13}\text{kg}$
• The acceleration due to the comet’s gravity: $\overrightarrow{a}=\text{−}\left(5.0\times {10}^{\mathrm{-3}}{\text{m/s}}^2\right)\widehat{j}$
• Philae’s mass: $M_p=96\text{kg}$
• Initial touchdown speed: ${\overrightarrow{v}}_1=\text{−}\left(1.0\text{m/s}\right)\widehat{j}$
• Initial upward speed due to first bounce: ${\overrightarrow{v}}_2=\left(0.38\text{m/s}\right)\widehat{j}$
• Landing impact time: $\text{Δ}t=1.3\text{s}$

Strategy

If we define a system that consists of both Philae and Comet 67/P, then there is no net external force on this system, and thus the momentum of this system is conserved. (We’ll neglect the gravitational force of the sun.) Thus, if we calculate the change of momentum of the lander, we automatically have the change of momentum of the comet. Also, the comet’s change of velocity is directly related to its change of momentum as a result of the lander “colliding” with it.

Solution

and just after was

Therefore, the lander’s change of momentum during the first bounce is

Notice how important it is to include the negative sign of the initial momentum.

Now for the comet. Since momentum of the system must be conserved, the comet’s momentum changed by exactly the negative of this:

Therefore, its change of velocity is

Significance