Collisions In Two Dimensions

The purpose of this lab is studying about the momentum and energy of two ball during collision.
In the first section, we need to watch the steel ball impacting another steel ball and determine the energy and momentum. Therefore, we set up a flat plate and collect the motion of two balls with camera.

data:

mass of steel ball: 115.5 g

mass of aluminum ball : 72 g

All of first, we make the steel ball to impact another ball.

To determine the position and velocity of two balls, we use program to points two balls in each half second. And then, we can calculate their velocity with computer.

From this table, we can make a graph to describing the shape how their motion is in x,y dimensions.

From this graph, we get the velocity of two balls in two dimensions,

and we can calculate their momentum:

After studying, we are able to see that the total kinetic energy decreases, and the momentum changes a little.

For the second part, we use the aluminum to impact the steel ball.

And then we do the same thing to determine the velocity of two balls.

Thus, we get the table:

From this table, we can make the graph:

and then, we calculate the momentum of the two balls,and we found the two momentum is big but it is all right, so there may be some thing wrong. But the kinetic energy still decreases.

conclusion, the momentum of the system does not change much when collision, but the kinetic energy will decreases.

Impulse Momentum ctivity

In this lab, our purpose is finding the relationship between impulse and momentum on the same object.However, we need to review the definition about impulse. Impulse combines the applied force and the time interval over which that force acts.J=Ft
And momentum is the product of the mass and velocity of an object.
j=mv
Therefore, we tried to measure impulse and momentum on a object in elastic collision and inelastic collision.

And then, we made the graph that record the force in respect of time, so that we can determine the impulse, and we also get the changed velocity and the mass, so we also get momentum.

From this graph, we discovered the impulse and momentum are almost same.

And, for  inelastic collision, we let the cart to impact the rubber so that the cart would not turn back after collision.

And we measure the impulse and momentum on a object again, so we got the graph:

From the graph, we also discovered that they are almost same.

Therefore, when the object impact with a wall that almost not move, the impulse and momentum are almost same, whatever it is elastic collision and inelastic collision.

Magnetic Potential Energy

In this lab, our purpose is finding an equation for magnetic potential energy.
As the picture shows, we set a cart on a air track so that there was not friction between cart and track.

Because the potential energy is caused by a force F for any system that has a non-constant PE, we made a relationship:

The r is the distance between cart and metal.

For making the relationship more clear, we need to apply different forces on cart and check each r. For measuring r, it is easy to do with ruler, but for the force applying on the cart, we need to use other approach. We use the gravity to apply. Because of the equation, F= mgsinx, we could find the angle and the mass of the cart, so that we can get the force. And then, we made a graph: 

From the graph, we can derive the equation:

and then, we could use integral to get the PE.

Works acting on a spring system

In this lab, we were going to study about the energy in spring system.
As the picture shows, we set the spring holding a mass. The motion sensor was below the mass for measuring the velocity and the position of the mass. The force sensor hold the spring for measuring the elastic coefficient.

 Therefore, we need to figure out what kinds of energy will be exist on the spring, and how they interact together.

1. Kinetic Energy
2. Static Energy
3. Elastic Potential Energy

First of all, we need to know the kinetic energy of the mass. We apply the equation with mass and velocity:

And then, we need the static energy and apply the equation with the velocity and mass:

At the last one, we also need to know the elastic potential energy and apply the equation:

However, we still did not know the elastic coefficient k. Thus, we measured the position of the non-stretched mass and the force applying to the force censor  And then, we added some mass to the spring so that the spring could be stretched longer, and we measured the new position and the new force applying to the force censor. Therefore, we could use this equation to get k.

And we can use this to find the elastic potential energy. And then, we make a table to record the number and a graph to show how they changing. For readability, we make a parameter for total energy.

From those pictures,we could discover that the total energy was a constant even though it was not perfect, so we can say the even though the energy always change, the total energy is unchangeable except there is another object applies work on it.

Work and Kinetic Energy

The lab we just did today is finding the relationship between work ad kinetic energy.
First of all, we need to set up a modal to find the equation for kinetic energy.

As the pictures show above, we connected a car and the force sensor that is on one side of track with spring and set the motion sensor on the other side, so we were able to measure velocity of car and force that applied on the car. And then, we put a wooden block on the track and put the spring on the block in order to reduce the friction from track to spring. 

For studying the work and kinetic energy, we need to know how much work the car had done.

we created a graph that represent the force and car's position.

Therefore, the area below line is work the car had done.

Now, we also need to create a line that describes kinetic energy:

As what we can see, the work line and kinetic energy line is almost overlapping together. Thus, the relationship is work=kinetic energy.