# Car Crash Physics: Velocities & Energy Lost in Collision

• zachk19
In summary, the situation involves a collision between two cars, one of which is pushed off a 40 meter cliff. The drivers were rivals for a woman's affections, and the incoming driver claims his brakes failed. The local District Attorney wants an expert witness to comment on the physics of the case. The parameters include the mass, coefficients of friction and elasticity, speed limit, distance, and angles of the cars and road. The incoming car careened across the street, and the witness must determine if the alibi holds up.
zachk19
I need to know the velocities before and after the collision and the engery lost. I have some of it figured out I am just stuck and could use some help. Here is the entire problem.

The situation: a patron has just entered his car after lunch in the parking lot of the Cliff-Side Café. Suddenly, another car comes careening from the road across the street. The second (incoming) car smashes into the parked car, sending it (and its occupant) flying off the cliff. The second car itself comes to a stop, and its occupant, though shaken, is essentially unhurt. The driver of the incoming car claims his brakes failed coming down a hill, so he was unable to avoid the collision (his brakes are so damaged from the collision that they give us no information). To complicate matters, the two drivers were rivals for the same lady’s romantic affections. Given the physical parameters of the situation, does the alibi of the incoming driver hold up?
The local District Attorney is prosecuting the case as a homicide. The D.A. wants you to testify as an expert witness (think “CSI”). You are not to render a “guilty” or “not guilty” verdict, though; rather, you are to comment on the physics of the case.
• Height of the cliff: 40 meters
• Horizontal distance (from base of cliff) of crashed car: 30 meters
• Mass of each car: 1000 kg
• Coefficient of static friction for parked car: 1.0
• Coefficient of kinetic (sliding) friction for parked car: 0.50
• Distance cars slide (during collision) before parked car falls off cliff: 2.0 meters
• Coefficient of rolling friction for incoming car: 0.020
• Diameter of tires: 0.60 meters
• Mass of individual tire: 20 kg
• Coefficient of elasticity (during collision): 0.75
• Speed limit of road: 25 mph (40 kph)
• Cross-sectional area of incoming car: 1.4 m by 1.6 m
• Coefficient of drag: 0.38
• Density of air: 1.293 kg/m3
• Distance from base of hill to collision site: 50 meters
• Angle of hill: 10 degrees
• Length of hill (along slope): 18 meters
• Initial velocity of car starting down hill: 5mph (2.24m/s)

Last edited:
melissa vega
zachk19 said:
another car comes careening
Why and how would a car be cleaning the hull of a ship? Oh, you mean careering!
It is a requirement on this forum that you post your own attempt at a solution, and any equations you believe to be relevant.

## 1. What factors affect the velocity of a car during a collision?

The velocity of a car during a collision is affected by several factors, including the initial velocity of the car, the mass of the car, the angle of impact, and the presence of any external forces such as friction or air resistance.

## 2. How is kinetic energy lost in a car crash?

In a car crash, kinetic energy is lost through deformation of the car's structure and the conversion of kinetic energy into other forms of energy, such as sound and heat. This loss of kinetic energy is what causes the car to slow down and come to a stop.

## 3. What is the difference between elastic and inelastic collisions?

In an elastic collision, kinetic energy is conserved, meaning that the total amount of kinetic energy before the collision is equal to the total amount of kinetic energy after the collision. In an inelastic collision, some of the kinetic energy is lost, resulting in a decrease in the overall velocity of the objects involved.

## 4. How can the concept of momentum be applied to car collisions?

Momentum is a measure of an object's mass and velocity, and it is conserved in a collision. In a car crash, the total momentum of the cars before the collision is equal to the total momentum after the collision. This can help to determine the velocities of the cars after the collision.

## 5. Is it possible for a car to come to a complete stop during a collision?

Yes, it is possible for a car to come to a complete stop during a collision. This can occur in an inelastic collision, where the kinetic energy is converted into other forms of energy, causing the car to come to a complete stop. However, in most collisions, some residual kinetic energy will still be present, even after the car has come to a stop.

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