# Calculating Impulse and Energy in a Car Collision

• MooPhysics
Thank you again for your help.In summary, two cars collide at a cross intersection, with the first car accelerating north for 10 seconds before being hit by the second car heading west. The cars stick together and slide off at a given final velocity. In order to determine the energy transformed into heat and the impulse of the first car's engine, vector equations for momentum conservation must be used. The initial velocity of the first car can be assumed to be 0 since it was initially at rest. The question also provides the masses of both cars and the final velocity of the combined system.
MooPhysics

## Homework Statement

A car initially at rest accelerates North for 10seconds. At 11seconds a second car heading west at (Time given in Km/h) collides with the first car at a cross intersection. The cars stick together and slide off across the intersection at (Vf given in KM/h). How much energy was transformed into heat? What is the Impulse of the first cars engine?
Mass of Car1 (Given in kg) (m1)
Mass of Car2 (Given in kg) (m2)
Velocity of Car 2 (v2)

## Homework Equations

m1v1=(m1+m2)v2
I=p (Change in momentum p)
p= m*v (Change in Velocity)
F*t=m*v3. Attempt
My question is: How do I figure out the velocity of the first car? I have tried v1=(m1+m2)v2/m1 but I am unsure if I am on the right track due to the car1 accelerating. Would the initial velocity for Car1 be vi=0 due to the car starting off at rest? I can't seem to work out the acceleration due to not having the distance given to me. Is there a formula I may have not considered here? I have a feeling I need to work backwards, but not sure where to start.

When the question asks about energy to heat, is it talking about Kinetic Energy. I thought some of the energy would have been absorbed do to the collision?

Can you post the problem exactly as it was given to you? Were you given any numbers? If so, what are they? Time is not usually given in km/h.
Your attempt at a solution assumes motion in one dimension. This is not the case here. You need to conserve momentum in two dimensions and write down some vector equations.

The question is:

Initaially at rest, a car (mass= 1240kg) accelerates north from a set of traffic lights at a constant rate for 10s. 11 seconds after starting to accelerate it crosses an intersection and is hit by a second car (mass=1124kg) heading west at 65km/h. The two cars stick together and slide off from across the intersection at 32km/h. How much energy was transformed into heat, damage or sound in the collision and how much impulse did the engine of the first car provide while it was accelerating?

MooPhysics said:
unsure if I am on the right track due to the car1 accelerating.
When the collision occurs, what parameters determine the outcome? Can it matter what the history is leading to those parameters?

You quoted a momentum conservation equation for coalescence, but remember momentum is a vector. So that is really two equations. You know the final speed, so how many unknowns do you have in those two equations?

Oh I see where I went wrong! Thank you for your help. I don't know why, but I didn't even consider it to be a 2 dimension. I think I have all the information I need to answer this now.

## 1. How do you calculate the impulse in a car collision?

To calculate the impulse in a car collision, you will need to know the mass of the car, the initial velocity of the car, and the time of impact. The formula for impulse is mass x change in velocity. So, you will need to calculate the change in velocity by subtracting the final velocity from the initial velocity, and then multiply it by the mass of the car.

## 2. What is the relationship between impulse and momentum in a car collision?

Impulse and momentum are directly related in a car collision. The impulse is equal to the change in momentum, as momentum is defined as mass x velocity. This means that the impulse in a car collision will be equal to the force applied to the car multiplied by the time of impact.

## 3. How do you calculate the kinetic energy in a car collision?

To calculate the kinetic energy in a car collision, you will need to know the mass of the car and its velocity. The formula for kinetic energy is 1/2 x mass x velocity squared. This means that the kinetic energy will increase as the velocity of the car increases.

## 4. What is the difference between elastic and inelastic collisions in terms of energy?

In an elastic collision, the kinetic energy is conserved, meaning that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound. This means that the total kinetic energy after the collision will be less than the total kinetic energy before the collision.

## 5. How does the conservation of energy apply to a car collision?

The conservation of energy applies to a car collision in that the total energy before the collision (kinetic energy + potential energy) will be equal to the total energy after the collision. This means that some of the kinetic energy will be converted into other forms of energy, such as sound or deformation of the car, but the total energy will remain the same.

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