Suburu WRX and a Honda Accord have collided at an intesection

[brightesthalo]

A suburu WRX and a Honda Accord have collided at an intesection. The suburu was initially traveling north. The honda was traveling west, about to initiate a right hand turn.

Obsercation of the scene of the accident and interviews with witnesses yeilds the following information:
1. The driver of the honda was a 52 yr old man of average build
2. The driver of the suburu was a 24yr old man of average build
3. After the impact the two vehicles traveled as one object
4. A witness states that neither driver appeared to break prior to the collision
5. The length of the skid was 12.8m in a direction N 7degrees W
6. The mass of the honda is 1400kg
7. the mass of the wrx is 1200kg
8. it was a dry day and the coefficient of friction between the tyres and the road is 0.6
9. the road is straight and flat
10. a witness states that the honda was stationary at a stop sign prior to entering the intersection
11. The beginning of the skid mark was 6m from the stop signDetermine the following:
a) was the suburu exceeding the 80km/h speed limit?
b) was the suburu visible to the driver of the honda before they initiated the turn?

*make sure u state all assumptions you have made
**the visibility of a car for a person with 20/20 vision is 1375feet and for a person with 20/50 vision is 550 feet.

 

[J77]

You need to show some of your working for help...

Although, I can say that (1) and (2) probably won't add too much to the answer

 

[andrevdh]

What I would do is use the work kinetic energy theorem to calculate their combined velocity just before they started skidding. Then use momentum conservation for the collision to calculate the velocity of the suburu just before the collision.

 

[brightesthalo]

how would i use the theorem before they started skidding though?

 

[andrevdh]

You use the theorem for the skidding part only.

 

[brightesthalo]

ok. and what abot the care that entered the intersection (6m away at the stop sign) does that information seem relevant?

 

[J77]

ok. and what abot the care that entered the intersection (6m away at the stop sign) does that information seem relevant?

That's one of the cars involved in the crash - you could probably take it to be stationary, or 10kph...

 

[andrevdh]

To be honest I myself will just ignore it since I have no idea what to do with it (only God and maybe high speed photography will enable one to know how to take that into account) and use momentum conservation for the rest. The skid marks were produced probably (a little bit after the collision) due to someone who had the sense to slam on his brakes (delayed reaction time) or the wheels dragging due to failure?

 

[J77]

To be honest I myself will just ignore it since I have no idea what to do with it (only God and maybe high speed photography will enable one to know how to take that into account) and use momentum conservation for the rest.

I wouldn't ignore it - if you do, the Suburu will have nothing to crash into

 

[brightesthalo]

hmm i see my homework as a bit ambuguous haha damn homework

 

[brightesthalo]

i meant ambiguous

 

[brightesthalo]

i still seem to be lost on this question.

 

[brightesthalo]

can anyone give me some extra help?

 

[J77]

Well, you have two objects which you know the mass and velocities of; the impact at right angles; they travel as a single object with which you know the mass and can work out the velocity; you know the distance traveled to zero velocity after the collision; this should give an average deceleration which you can compare to frictional forces...

 

[andrevdh]

Apply the theorem to the skidding part of the collision - Assumption: The wrecks came to a halt at the end of it. Show us your results in your next post.

My thoughts on the inclusion of the 6 meters is that since the distance is so large one can safely assume that there were no interaction forces with the road present during the collision. This means that momentum will be conserved for the collision part of the incident.

 

[brightesthalo]

thing is i don't know the velocities of the two objects all I am given is the mass of them both, the angle which they skid as one and how many metres they skid

 

[brightesthalo]

im only given the skid mark and the distasnce of it i don't have any velocities

 

[J77]

thing is i don't know the velocities of the two objects all I am given is the mass of them both, the angle which they skid as one and how many metres they skid

...but you need to work out the velocity of the Suburu.

The Honda has just set-off from being stationary, so you could assum it to have zero velocity or, say, 10kpm - didn't we do this yesterday

 

[andrevdh]

Have you done the work-kinetic energy theorem yet?

 

[brightesthalo]

KE = 1/2 mv2 right?
we never got taught the work-kinetic energy theorem which is annoying (as u can see iv only started physics and I am not very good at it)

 

[andrevdh]

Ok let's do the skidding part with kinematics then.

What force is causing the wrecks to decelerate during the skidding part?

Can you calculate the magnitude of this force?

 

[brightesthalo]

the force of friction and i am guessing they would be trying to brake during collision

oh man i must really suck

 

[andrevdh]

When a car brakes the wheels slide in stead of roll over the road. Guess what happens when an object slides over a surface? It experiences a frictional force coming from the surface. Try and calculate the magnitude of this frictional force for the combined wrecks.

 

[brightesthalo]

N=W
= mg
= 1200 x 9.8
= 11760N

F = u W
= 0.6 x 11760
= 7056N

Am i on the right track?

 

[brightesthalo]

oh hang on i need combined wrecks
not just suburu damn

 

[brightesthalo]

so i add 1200 and 1400 then x 9.8 = 25480N
then divide .6 = 15288N

? I am not doing this right am i?

 

[andrevdh]

Seems fine. Now calculate their acceleration and their initial speed, that is their combined speed before the skidding started.

 

[brightesthalo]

a = F/m
= 15288/2600
= 5.88m/s

as for initial speed how do i calculate that?

 

[brightesthalo]

would that be using v2=u2 +2as somehow?

 

[andrevdh]

That is correct.

 

[brightesthalo]

do i have to assume the distance of the suburu seeing as it hasn't been given

 

[andrevdh]

The cars are mangled together and are sliding as a unit.

 

[brightesthalo]

still won't help me decide whether the suburu was going faster than 80 km/h would it?

 

[andrevdh]

The answer need to be appoached in several steps. This is one of them before you will be able to answer that question.

The combined wrecks start with some speed v and are decelerated to zero by the frictional force. What do you get their initial speed?

 

[brightesthalo]

i would use the equation i stated above to find the combined wreck speed in the 12.8 m.
i tried that and got 12.26 m/s ---> 44.136km/h

that right?

 

[andrevdh]

I get the same.

Now you can calculate the momentum of the combined wrecks after the collision. What will the direction and magnitude of this vector be?

 

[brightesthalo]

so it would be p=mv
= 2600 x 12.26
= 31876
??

 

[andrevdh]

Units of the calculated momentum? What would the direction of the vector be?

 

[brightesthalo]

? ok now I am lost here I am gussin 7 deg

 

[andrevdh]

Yes that is seven degrees west of north. The direction of the momentum vector is determined by the direction in which the object is moving. In this case the direction in which the wrecks are sliding.

What will the components of this momentum vector be in the north-south and east-west directions?

 

[brightesthalo]

would this by any chance be wher sin tan cos would be used? if not then i don't really know

 

[andrevdh]

Yes. The components of a vector is calculated with the angle that it makes with one of the chosen perpendicular directions, seven degrees, and the magnitude (size or length) of the vector, that is 31786 kgm/s in this case.

 

[brightesthalo]

maybe i should sleep on it a bit its 1:10 am here so sorry for bothering u . ill try tacle this in the morning ( don't know how successful ill be)

 

[brightesthalo]

actually ill stay a little longer i really need this done

 

[andrevdh]

It is time for me to go home also. I might be online in about 16 hours time.

What you need to do is calculate the components of this vector and compare it with the momentum vectors before the collision. Since momentum is conserved the components need to be the same in both directions before and after collision.

 

[brightesthalo]

how did u work that out?

 

[brightesthalo]

ok that's ok itl be too late i have class tomorrow
thank u for your help anyhow
i appreciate it very much

 

[andrevdh]

You need to calculate the components of the momentum after the collision, p_a. These two components are such vectors that when added together will produce the vector p_a. They also form the sides of a right angle (its base and perpendicular) as indicated in the attachment, while the vector p_a are the hypotenuse of the triangle.