Momentum Change in Perfectly Inelastic Collision: Comparing Cars and Trucks

[jabbie3]

Homework Statement

A compact car and a large truck collide head on and stick together (perfectly inelastic collison).

Which vehicle experiences the larger momentum change?

Which vehicle experiences the larger acceleration during the collision?

Explain your answers.

Homework Equations

p=mv
I=Ft

The Attempt at a Solution

I think that the truck has a larger momentum change because, first of all, it is conserved, so p=p_final-_initial

Assuming the velocities are the same, only the mass should affect the momentum. So that's why I thought the truck has a larger momentum change.

But I'm not sure..I look at I=Ft and the forces are equal, and so is the time..So would they have equal change in momentum?

HELP! thanks!

 

[Carid]

The truck will carry on in the same direction with modified velocty, whereas the unfortunate car will find itself going backwards. Now which one has suffered the largest change in momentum? acceleration?

 

[nlightner]

I would approach this problem by first examining the definition of momentum and the equations involved. Momentum is defined as the product of an object's mass and velocity, represented by the equation p=mv. In a perfectly inelastic collision, the two objects stick together and move with a common velocity after the collision. This means that the final velocity for both the car and the truck will be the same, and the only difference will be in their masses.

Therefore, the truck, which has a larger mass, will experience a larger change in momentum compared to the compact car. This can also be seen by looking at the equation p=mv, where the mass is directly proportional to the momentum. So, if the mass of the truck is larger, its momentum change will also be larger.

As for acceleration, we can use the equation I=Ft, where I represents the change in momentum, F represents the force, and t represents the time. Since the two vehicles are colliding head on and sticking together, they experience the same force and same time during the collision. This means that they will have equal acceleration during the collision.

To summarize, in a perfectly inelastic collision between a car and a truck, the truck will experience a larger change in momentum due to its larger mass. However, both vehicles will experience the same acceleration during the collision.