# Antique Road Show Physics Problem: Calculating Final Velocity of Colliding Carts

• cooper43
In summary, the conversation discussed the scenario of two carts colliding and sticking together, with different masses and velocities. The experts determined that conservation of momentum should be used, and the resulting calculation showed that the carts would move to the left with a velocity of 0.33 m/s.
cooper43

## Homework Statement

I was wondering if anybody might help me on this UNLESS i did this correct, but I'm not totally sure.

Well here's the question.

Jorge and Elizabeth are both going to the Antique Road show on PBS. Jorge pushes an antique desk weighing 300kg on a car to the right, while Elizabeth pushes a similar cart to the left with a dresser weighing 225kg. The mass of each cart is 500kg and Jorge pushes his with a speed of 3.0m/s and Elizabeth at a speed of 4.0m/s. If the cars collide and stick together then what is their final velocity and which direction are they headed?

KE=1/2*m*v^2
P=mv

## The Attempt at a Solution

Car 1
500kg+300kg=800kg
3.0 m/s to the left

KE=(.5)mv^2
KE=(.5)(800)(3.0)^2
KE=3600

Car 2
225kg+500kg=725kg
4 m/s to the right

KE=(.5)mv^2
KE=(.5)(725)(4.0m/s)^2
KE=5800

5800-3600=2200

KE=(.5)mv^2
2200=(.5)(mass of Car1 and 2, 1525kg)( v )^2

Solved using calculator

V=1.6986m/s to the right

Am I right?

Last edited:
Looks like you are using conservation of kinetic energy when you should be using conservation of momentum. Stick-together collisions are not elastic - kinetic energy is lost.

So should I be using P=mv?

You definitely should be using conservation of momentum. In collisions that aren't completely elastic (this one's not as the carts stick together) kinetic energy is not conserved as some energy is lost to heat.

What is conservation of momentum?

The law of conservation of momentum states that if no net external force acts on a system that the initial and final momentum of the system must be the same; hence, Pi = Pf

So i should use these

If so, which one?

i got 3.95082 with the first and
2.95082 with the second

Then put an mv on each side for each object that is moving.
mv + mv = mv (where all the m's and v's are different and perhaps should be numbered)
Put in the numbers and solve for the one unknown speed.

so is it
((M1*V1)+(M2*V2))/(M1+M2)
that way velocity is isolated?

Now I got -.000215

I'm moving on to the next question now

Cooper43, the equations you posted only apply in the case of a completely elastic collision. The scenario you've described appears to be completely inelastic.

Last edited:
I (think I) FOUNT IT!

Last edited by a moderator:
Yes, that equation will suffice for the scenario described in the problem.

(800) (3) + (725) (-4) = (1525)V

V = -0.328 m/s?

they move to the left?

That's what I got. They move left with a velocity of v = 0.33 m/s. Good job!

Yes, finally. Thanks jgens :)

You're welcome!

## What is the Antique Road Show Physics Problem?

The Antique Road Show Physics Problem is a classic physics problem that involves two carts colliding with each other. The problem requires the calculation of the final velocity of the carts after the collision, given their initial velocities and masses.

## Why is this problem important in physics?

This problem is important because it helps us understand the concept of conservation of momentum and how it applies to real-life situations. It also helps us practice using the equations of motion and applying them to solve problems.

## What are the necessary information needed to solve this problem?

The necessary information needed to solve this problem includes the initial velocities of the two carts, their masses, and the coefficient of restitution (a measure of how much energy is lost during the collision).

## How do we approach solving this problem?

To solve this problem, we first need to identify the initial and final states of the system, and then apply the principles of conservation of momentum and conservation of energy. We also need to use the equations of motion to solve for the final velocity of the carts.

## What are some common challenges when solving this problem?

Some common challenges when solving this problem include correctly identifying the initial and final states of the system, understanding and applying the equations of motion, and taking into account factors such as friction and air resistance. It is also important to carefully consider the direction of the velocities and use proper units in calculations.

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