Solving a Problem: Combining Two Vehicles Masses

[c4iscool]

I can't figure out this problem. A 1000kg car traveling east at 3m/sec collides with and sticks to a vehicle traveling due west at 2m/sec. Immediately after the collision, the vehicular combination is moving due west at 1m/sec. the mass of the second vhicle is ? kg. How do I set this up?

 

[Doc Al]

What's conserved during the collision?

 

[c4iscool]

I think the mass would be conserved.

 

[neutrino]

I think the mass would be conserved.

Anything else? Think important conservation laws.

 

[c4iscool]

Are u guys getting at conservation of energy laws? But can I only get the velocity with that?

 

[Hootenanny]

Are u guys getting at conservation of energy laws? But can I only get the velocity with that?

I'll give you a clue, it starts with an 'M' and its not mass

 

[c4iscool]

conservation of matter

 

[Hootenanny]

conservation of matter

Thats the same as mass. Are you sure you know no other conservation laws? I'll give you another clue, its symbol is 'P'

 

[c4iscool]

I don't know of any others. sorry I'm a noob!=(

 

[c4iscool]

oh momentum

 

[Hootenanny]

I don't know of any others. sorry I'm a noob!=(

No problem . The law you need to use is 'conservation of momentum'. Have you heard of momentum before? Do you know how it is defined / how to calculate it?

 

[c4iscool]

is it m1v1=m2v2 or something?

 

[Hootenanny]

is it m1v1=m2v2 or something?

Thats the one. Initial momentum (the product of mass and velocity) must equal the final momentum. Take note that momentum is a vector quanitity, so direction matters.

 

[c4iscool]

but how do I figure out the final momentum without the mass?

 

[Hootenanny]

You can calculate the intial momentum. You know the final velocity. You know the two vehicles are stuck together. Can you formulate an equation using the above facts?

 

[c4iscool]

would the equation be (1/2)Massf(1)=(1/2)1000(3). or can I drop the 1/2 in front of the equation.

 

[Hootenanny]

would the equation be (1/2)Massf(1)=(1/2)1000(3). or can I drop the 1/2 in front of the equation.

Hmm. How about this taking east to be positive and letting M = 1000kg, m be the unknown mass, v₁ = 3, v₂ = -2 and v_f = -1;

$$Mv_{1} + mv_{2} = (M+m)v_{f}$$

 

[c4iscool]

is the mass about 2000 or 4000?

 

[Hootenanny]

is the mass about 2000?

I got the mass to be about 1333kg. Perhaps you have made an arithmetic error? If you show your working I'll see if I can see where you've gone wrong.

 

[c4iscool]

I just reworked it and now I have more!
(1000*3)+m(-2)=(1000+m)-1
3000-2m=-1000-m
4000=m

 

[Hootenanny]

Oh, I do apologise, the error is on my part . The mass is indeed 4000kg, which is what I intuitively would expect, but I made a silly error. It happens :tongue2: . Anyway you got the correct answer. Well done

 

[c4iscool]

thanks you so much!

 

[Hootenanny]

thanks you so much!

No problem and thank you for correcting me.