Center of Mass/Linear Momentum

In summary, the problem involves two cars (A and B) colliding at a traffic light, with car A being rear-ended by car B. Both cars then slide with locked wheels until the frictional force from the slick road stops them at distances dA = 5.3 m and dB = 3.4 m. The question is asking for the initial speeds of both cars at the start of the sliding, just after the collision, and the speed of car B just before the collision assuming linear momentum is conserved. Using the equation W = -1/2mvi^2 and momentum conservation, the initial speeds of both cars after the collision can be determined, and the speed of car B before the collision can be found
  • #1
Nikolan
5
0

Homework Statement


In the "before" part of Fig. 9-60, car A (mass 1100 kg) is stopped at a traffic light when it is rear-ended by car B (mass 1500 kg). Both cars then slide with locked wheels until the frictional force from the slick road (with a low μk of 0.21) stops them, at distances dA = 5.3 m and dB = 3.4 m. What are the speeds of (a) car A and (b) car B at the start of the sliding, just after the collision? (c) Assuming that linear momentum is conserved during the collision, find the speed of car B just before the collision.

(see attachment for image)


Homework Equations



(A = CarA, B = CarB)

PAi + PBi = PAf + PBf
(mA)vAi + (mB)vBi = (mA)vAf + (mB)vBf


The Attempt at a Solution



I've been sitting here looking blankly at this problem for about an hour now. I really have no idea where to start with this, I've tried a few things, but it always ends up giving me two unknown variables. Looking at another thread that was posted on this question, I realize that all the kinetic energy is transferred to thermal in the end, how does that help?

(https://www.physicsforums.com/showthread.php?t=82429)
 

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  • #2
Hi Nikolan, welcome to PF

For a) & b) think about one car at a time. After the collision, the work done by friction slowing the car will equal the decrease in kinetic energy of the car.
 
  • #3
Thank you very much!

I ended up taking what you said and applying it like this:

(Using this solution for both cars A and B)

Fk = (uk)FN to find force of friction.

W of Friction = (Fk)(D) = Kf - Ki = 1/2mvf^2 - 1/2mvi^2

to get:

W = - 1/2mvi^2 => sqrt(((-2)(W))/M) for initial speeds of both cars directly after impact.
I then used Momentum of Cars before = Momentum afterwards
or
Pai + Pbi = Paf + Pbf
mavai + mbmbi = mavaf + mbvbf

and plugging in relevant values to end up with initial speed of car B before collision.Again, thanks for your help! :approve:
 

1. What is the center of mass?

The center of mass is a point in an object or system that moves as if all the mass of the object or system were concentrated at that point. It is also the point where the object or system will balance if suspended from that point.

2. How is the center of mass calculated?

The center of mass is calculated by finding the weighted average position of all the mass in an object or system. This is done by multiplying the mass of each part by its distance from a reference point and then dividing the sum of these products by the total mass of the object or system.

3. What is linear momentum?

Linear momentum is a measure of an object's motion. It is the product of an object's mass and velocity. In other words, it is the quantity of motion an object has in a certain direction.

4. How is linear momentum conserved?

According to the law of conservation of momentum, the total momentum of a closed system remains constant. This means that the total amount of momentum before an event must equal the total amount of momentum after the event, as long as there are no external forces acting on the system.

5. How are center of mass and linear momentum related?

The center of mass and linear momentum are closely related because the motion of an object or system can be described in terms of the motion of its center of mass. Additionally, the center of mass is the point at which an object's or system's linear momentum can be said to be concentrated.

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