Really annoying physics A2 question! Don't have mark scheme!

Your best option is probably to conduct an experiment and collect relevant data, aka go into space and chuck rocks at Earth.

This question has really been annoying me, some one please help!

It's from the Edexcel GCE Salters Horners Physics PSA4 paper from 20th Jan 2004;

Q6)
As it moves through space, the Earth collides with small amounts of stationary material such as comet debris. After the collisions the pieces of material move with the Earth through space. As the Earth gives momentum to the material it collides with, it experiences a very small retarding force, and hence deceleration. Calculate this deceleration and comment on your answer.

Mass of extra material collected by the Earth each second = 7.0 kg
Speed of the Earth through space = 3.0 x 10^4 m/s
Mass of Earth = 6.0 x 10^24 m/s

Here is what I thought I would do;
Calculate the momentum of the Earth and the material before the collision, using p=mv

As the extra material is sationary it will have zero momentum - so the momentum before the collision will be just the momentum of the earth, I calculated this as 1.8 x 10^29 kgm/s

Now according to the conservation of momentum the momentum before must equal the momentum after - so from that I can rearrange p=mv to v=p/m. I will then use this to calculate the velocity at which the Earth moves off after the collision with the material. Then I can use acceleration = change in velocity/time taken to work out the deceleration.

But the problem is that the calculator not precise enough to take into account the new mass of the Earth - according to the calculator 6 x 10^24 + 7kg = 6 x 10^24!

Am I being really stupid and making this more complicated than it is or am I ment to use kinetic energy and assume it is all converted to to the speed?

Help!

You are on the right track when you set up the momentum before and after, correctly identifying that this collision is “sticky”.1.) mass of the earth x velcity of the earth = (mass of the earth mass of debris) x velocity of the earth after collision.If you use 7kg as the mass of the debris our calculator will give the answer as zeros for the final velocity. This is because calculators are not proficient enough to detect small changes.2)Comment: “the time frame I will be using in this question needs to be in the factor of x10^24, in order to get a measurerable change in the velocity.”3) now the mass of the debris becomes(7x10^24)kg this is where I have “waited” for 1x10^24 seconds. Since the rate of debris collision is 7, the mass accumulated becomes as shown above.4) now you can use momentum setup from part one to calculate the final velocity, which should be noticeably smaller than the original speed of the earth.5) once you have the initial and final velocities, and the time, to work out the deceleration, use SUVAT.(v-u)/t = aYour value should be very small.The marks should be awarded based on reasoning and not based on the final answer, as individual will get different answers based on what time frame they picked. So you must comment on the steps you have taking as you go along; stating what you are doing, assuming or taking into account.Hope this helps