Calculating Drunk Driver's Speed in a Collision

In summary, the problem involves a drunk driver's car colliding with a parked car, causing both cars to slide 39.5 m before coming to a stop. The mass of the drunk driver's car is 880 kg and the parked car's mass is 804 kg. Using the momentum equation for inelastic collisions, the velocity of both cars after the collision is found to be 16.9 m/s. By setting up a second equation with the initial and final velocities of the drunk driver's car, the initial velocity is solved to be 32.3 m/s.
  • #1
CaptFormal
33
0

Homework Statement



A drunk driver strikes a parked car. During the collision the cars become entangled and skip to a stop together. The drunk driver's car has a total mass of 880 kg, and the parked car has a total mass of 804 kg. If the cars slide 39.5 m before coming to rest, how fast was the drunk driver going? The coefficient of sliding friction between the tires and the road is 0.37.

Homework Equations



Δ(K + U) = Wnc


The Attempt at a Solution



I am having some difficulties setting up the problem correctly. Now, I know that the drunk driver's care will have KE but the parked car will not. I know that the Wnc = Fd which means that it will be the displacement of the vehicles (39.5 m) times the Force (0.37) of the sliding friction on the road. What I am a bit confused on is how does potential energy (U) play into this equation. Any assistance or suggestions will be greatly appreciated.
 
Physics news on Phys.org
  • #2
Because the cars become entangled, some energy is wasted as heat, thus you cannot use that equation.
A collision like this is called inelastic collision. Use the momentum equation for this.
http://en.wikipedia.org/wiki/Momentum has a short section on inelastic collisions
 
  • #3
By the way, the force of friction isn't 0.37; that's the coefficient of friction.
 
  • #4
Well, I was able to finally figure it out.

It seems as though I must first find the velocity of both the cars after the collision in order to solve for the initial velocity of the drunk driver's vehicle. Thus,

-uk(m)(g)(d) = mgh - 0.5mv^2

uk = sliding friction
m = mass
g = gravity
d = displacement

We are given the sliding friction, gravity, and displacement and mass cancels each other and PE will equal 0. Thus...

-(0.37)(9.8)(39.5) = 0 - 0.5v^2

v = 16.9 m/s

This is the velocity of both of the vehicles after the collision. So, I used this velocity to find the initial velocity of the drunk driver by the following process:

MaVa + MbVb = MaVa' + MbVb'

MaVa = mass and velocity of the drunk driver's car
MbVb = mass and velocity of the parked car

We are given Ma, Mb, and we just solved for Va and Vb. We also know that since the parked car is indeed parked that MbVb' is equal to 0. Thus:

(880)(16.9) + (804)(16.9) = (880)Va' + (0)

I solved for Va' and got 32.3 m/s which is the answer.

Thank you for all of your help. I do appreciate it.
 

FAQ: Calculating Drunk Driver's Speed in a Collision

1. What causes a collision between two vehicles?

A collision between two vehicles is typically caused by a combination of factors, such as driver error, road conditions, and vehicle malfunctions. It can also be caused by external factors such as weather conditions or objects on the road.

2. How can the severity of a collision be determined?

The severity of a collision can be determined by several factors, including the speed of the vehicles involved, the angle of impact, and the size and weight of the vehicles. Other factors that can affect the severity of a collision include the use of safety features like seat belts and airbags, as well as the type of vehicles involved (e.g. passenger car vs. large truck).

3. What are the most common injuries resulting from a collision?

The most common injuries resulting from a collision between two vehicles are whiplash, head injuries, and fractures. Other injuries can include cuts and bruises, broken bones, and internal organ damage. The severity and type of injuries can vary depending on the speed and force of the collision.

4. How can collisions between vehicles be prevented?

Collisions between vehicles can be prevented by following traffic laws, maintaining a safe distance from other vehicles, avoiding distractions while driving, and regularly maintaining and inspecting your vehicle. It is also important to be aware of your surroundings and adjust your driving according to weather and road conditions.

5. What should I do if I am involved in a collision between two vehicles?

If you are involved in a collision between two vehicles, the first and most important step is to ensure the safety of yourself and others involved. Call for medical assistance if needed and then contact the police to report the accident. It is important to exchange information with the other driver(s) and document the scene with photos and notes. Finally, contact your insurance company to report the accident and begin the claims process.

Similar threads

How to Calculate Speed of Head of Driver After Collision?
Replies
10
Views
2K
Initial velocity in an inelastic collision
Replies
4
Views
2K
Inelastic Collision of drunken driver
Replies
7
Views
2K
Car Crash Analysis: Analyzing Friction & Speed
Replies
9
Views
4K
Calculating Initial Speed in an Inelastic Collision with Friction
Replies
5
Views
3K
Car Crash Physics: Velocities & Energy Lost in Collision
Replies
1
Views
3K
Was the Second Driver Speeding in the Collision?
Replies
10
Views
1K
Cars Collide on a Hill, Conservation of Momentum
Replies
7
Views
2K
Coefficient of friction and drunk driver
Replies
2
Views
4K
Calculating Separation of Cars in a Convoy Moving at Max Speed
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top