# Conservation of Momentum, a Totally Inelastic Collision

• mvl46566
In summary, the problem involves a 950kg car colliding with a 450kg hay wagon on an icy, frictionless patch. Both objects have initial velocities, and if they stick together after the collision, the final velocity needs to be calculated. Using the equation m1v1 (initial) + m2v2 (initial) = vf (m1+ m2), the solution involves finding the x and y components of the initial velocities and plugging them into the formula to solve for the final velocity. The x and y components of the final velocity can be found by multiplying the total mass of the two objects by the sum of their respective x and y components of the initial velocities, and dividing by the total mass.
mvl46566

## Homework Statement

A 950kg compact car is moving with the velocity ⃗v1 = 32 ˆx + 17 ˆy m/s. It
skids on an icy, frictionless patch and collides with a 450kg hay wagon
moving with velocity ⃗v2 = 12ˆx +14ˆy m/s. If the two stay together,
what is their velocity?

## Homework Equations

m1v1 (initial) + m2v2 (initial) = vf (m1+ m2)

## The Attempt at a Solution

I realize this is a totally inelastic collision and I need to use the above equation to solve. However, I don't know how to change the vector components into a number that can be plugged into the formula. I have tried adding the vector components of both velocities (x+x, y+y) but the answers I am getting do not sound right. I tried doing this because I figured if I know the numbers for the masses I can factor them out and have the vectors being added to together, but I don't think this is the solution. Please help!

Show your calculations. Try this one.
m1*v1x + m2*v2x = (m1+m2)*vfx.
Similarly for y components.

I would approach this problem by first converting the given velocities into their corresponding components in the x and y directions. This can be done using basic trigonometry and the given magnitudes and angles. Once the velocities are in their component form, I would then use the conservation of momentum equation as stated in the homework to solve for the final velocity.

To start, I would label the compact car as object 1 and the hay wagon as object 2. Using the given masses and velocities, I would first calculate the momentum of each object in the x and y directions.

For object 1:
Px1 = (950kg)(32m/s) = 30400 kgm/s in the x-direction
Py1 = (950kg)(17m/s) = 16150 kgm/s in the y-direction

For object 2:
Px2 = (450kg)(12m/s) = 5400 kgm/s in the x-direction
Py2 = (450kg)(14m/s) = 6300 kgm/s in the y-direction

Next, I would add the momenta of each object in each direction to find the total momentum before the collision.

Px (initial) = Px1 + Px2 = 35800 kgm/s in the x-direction
Py (initial) = Py1 + Py2 = 22450 kgm/s in the y-direction

Since this is a totally inelastic collision, the two objects will stick together after the collision and move with a combined velocity. This means that the final momentum in each direction will be the same for both objects.

Using the conservation of momentum equation, I can set the initial momentum equal to the final momentum and solve for the final velocity.

(m1 + m2)vf = Px (initial) + Py (initial)
(950kg + 450kg)vf = 35800 kgm/s + 22450 kgm/s
1400kg vf = 58250 kgm/s

Solving for vf, we get:
vf = 41.61 m/s in the x-direction
vf = 41.61 m/s in the y-direction

Therefore, the final velocity of the combined objects after the collision is 41.61 m/s in the x-direction and 41.61 m/s in the y-direction. This can also be expressed in vector form as ⃗vf = 41.61 ˆx

## What is conservation of momentum?

Conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant over time, regardless of any external forces acting on the system.

## What is a totally inelastic collision?

A totally inelastic collision is a type of collision in which two objects collide and stick together, resulting in a decrease in kinetic energy and the formation of a single, larger object.

## How does conservation of momentum apply to totally inelastic collisions?

Conservation of momentum applies to totally inelastic collisions because, even though the kinetic energy decreases, the total momentum of the system must remain the same. This means that the total mass and velocity of the objects before and after the collision must be equal.

## What are some examples of totally inelastic collisions?

Some examples of totally inelastic collisions include two cars colliding and sticking together, a ball hitting and sticking to a wall, and two drops of water merging into one larger drop.

## Why is the concept of conservation of momentum important in science?

The concept of conservation of momentum is important in science because it helps us understand and predict the motion of objects in various scenarios, such as collisions. It is also a fundamental law that governs the behavior of matter in the universe.

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