# Velocity after 2 cars collide

1. Sep 6, 2015

### Entr0py

1. The problem statement, all variables and given/known data
A 2000-lb car traveling north at 60 mph collides with a 5000-lb car traveling east at 40 mph. The cars stick together after the collision. Find the velocity (magnitude and direction) of the cars just after the collision.

2. Relevant equations
conservation of linear momentum

3. The attempt at a solution
Firstly, I need to find the masses of each car. Car 1 has weight of 2000 lbs and has a mass of (2000/32.2) about 62 slugs. Car 2 has weight of 5000 lbs and has mass of (5000/32.2) about 155 slugs. That said, the initial momentum of car 1 equals m(1) times v(1) or (62 slugs times 60 mph) = 3720 slug-m/h. Initial momentum of car 2 equals m(2) times v(2) or (155 times 40 mph) = 6200 slug-m/h. So the total initial momentum is 9920 slug-m/h.

The final momentum of the cars= (total mass of cars since they stick together) times (new velocity) which equals 217v, so v= 9920/217 or 45.7 mph. To find the direction of velocity after collision, wouldn't I do arctan(40/60) = 33.7 degrees NE.

Now I must be doing something wrong because in the back of the book, the answer is 33.3 mph at 31 degrees NE. So i can't figure out what I'm doing wrong.

2. Sep 6, 2015

### Staff: Mentor

You cannot add momentum in different directions linearly.

Where is the point in the conversion from one weird unit to another? The masses will cancel anyway, so working with lb everywhere will work. Conversions just introduce rounding errors.

3. Sep 6, 2015

### Ray Vickson

(1) Nevermind the units; just use masses of m1 = 2 and m2 = 5. Converting to thousands and slugs serves not purpose in this problem, since you are just multiplying and later dividing by a constant.
(2) The initial momenta of the two cars are VECTORS pointing in different directions, so you need to represent them by their x- and y- coordinates; You cannot simply add up their magnitudes.

4. Sep 6, 2015

### Entr0py

You're RIGHT, momentum is a vector. Oh shucks

5. Sep 6, 2015

### BvU

Hello S,

Why you want a mass in slugs is a mystery to me. Never mind.
Momentum is a vector. You can't add the components like this: they are at right angles to each other !

So do a vector addition and use Pythagras to find the total momentum.
The tangent of the direction angle is the y momentum divided by the x momentum

 slow typist: Ray was faster and you already saw what was to be done. All is well.

6. Sep 6, 2015

### Entr0py

don't I need their mass in slugs to use in p=mv?

7. Sep 6, 2015

### BvU

is slugs * mph any better than lb * mph ?

But as Ray says, lb, slugs or stones, or the usual kg: you are multiplying them in and then dividing them out again later on

8. Sep 6, 2015

### Entr0py

Oh ok. So i calculated the net momentum by pnet= p1 + p2 and that gave me 233. Then to find the resultant velocity I I did v=(233)/7 = 33.3 mph. Now I can't seem to find the direction. I thought it would be arctan (3) but thats not correct.

9. Sep 6, 2015

### Entr0py

I figured the answer out. Now I need to spend quite some time figuring out and learning THE PROCESS to get the answers. Knowing that momentum IS a vector it has vertical and horizontal components. So initial momentum^2= P(ix)^2 + p(iy)^2 and so p(i)=sqrt of all of that. Then to find p(f) i need to do the same thing but note that mass=M=combined mass of the two cars. From momentum conservation I know that the COMPONENTS of initial and final momentum equal one another. Doing this I can solve for final vertical velocity and final horizontal velocity. Knowing these I add the sum of their squares and then sqrt that to find final velocity vector. To find its direction I just do arctan (final vertical velocity/final horizontal velocity). HOWEVER, I'm still confused why I can just use pounds instead of slugs in this question. Since i need to find the momentum of each car I need to use their mass (but pound is a measurement of weight and slugs is a measurement of mass). That's why I converted pounds into slugs. because isn't momentum measured in kgm/s in SI units? That is mass times velocity, so how would (pounds miles an hour) be just as useful as (slugs miles and hour) if slugs measure mass and pounds measure weight?

10. Sep 6, 2015

### haruspex

Why 3? It's the momentum ratio you want, not the velocity ratio.

11. Sep 6, 2015

### haruspex

If each car were exactly twice the mass given, would it change the answers?

12. Sep 6, 2015

### Entr0py

I figured out my mistake.

13. Sep 6, 2015

### Entr0py

No it wouldn't. Does that mean i say p=(lb)(mph)?

14. Sep 6, 2015

### Staff: Mentor

p=mv is independent of units. You can use lb*mph, you can use kg*m/s, you can use (multiples of your body weight)*(average speed of an unladen European swallow) - it does not matter.
You just have to be consistent in the calculation.

15. Sep 6, 2015

### Entr0py

I'm sorry, I understand that you and the other mentors are trying to help me understand that momentum is IND of units used. it's just isn't a pound a measurement of weight which measures force? Then how can i use p=(measurement of force)(rate). I understand that rate is just velocity which is change in displacement. I get that. But I'm frankly stuck on why I can use a measurement of force in place for a measurement of mass.

16. Sep 6, 2015

### Staff: Mentor

pound is a unit of mass.
pound-force (sometimes called "pound" as well which is wrong) is a unit of force.

17. Sep 6, 2015

### Entr0py

THANKS for the clarification. So when the author says a car of 2000 pounds he is just saying that this car has a MASS of 2000 pounds not that the force of gravity acting on it is 2000 FORCE-POUNDS?

18. Sep 6, 2015

### NickAtNight

The author should have been more precise. Usually we designate $lb_f and lb_m$ to distinguish between the two.

Remember : $1 lb_f = 1 lb_m$ so lbs could be either units of force or units of mass.

Sometimes we use this equation $F = \frac{m * a}{g_c}$ where the $G_c$term is used to convert us from slugs to$lb_m$

19. Sep 6, 2015

### Entr0py

where gc is 32.2 ft/s^2?

20. Sep 6, 2015

Correct