12/2/2014 SHM

Purpose:

The purpose of this experiment is to calculate the period of half circle piece of cardboard.

Experiment:

The first part of our experiment is cut out a half circle from cardboard to use for our simple harmonic motion.

Once we cut out the half circle we had to calculate the inertia from the the top and bottom of the half circle.

We used to calculus to solve inertia from the center of mass and then made the proper shifts to find the inertia from pivot of top and bottom.

Here is our calculation for inertia from center of mass.

We then created a formula to calculate the period of the using SHM.

The mas of our half circle is 0.0058kg with a radius of 0.1075.

Once we had both formulas we then predicted the period of SHM from the top as 0.714 seconds and from the bottom as of 0.613 seconds.

Here is a picture of our calculation.

 Here is a picture of are system we used a motion sensor to measure the periods which we found for the bottom 0.764s and from the top 0.694s

For the period from the pivot on the bottom we where off by 6% and for the period with the pivot on the top we where off by 11%.

11/25/2014 Mas Spring Oscillations Lab

Purpose:

For this lab we are going to test how the period of a spring with hanging mass is affected by the spring constant and or the hanging mass.

Experiment:

In this lab the class separated into eight groups where four groups would share there measured information with in the four groups.

Each group of the four had unique spring with separate spring constant values. To make sure we all usable reading we had to make sure all our spring weight was the same so every one had to add weight to our system to make sure the values where good. We did this by taking the heaviest spring and taking a third of the mass  so all one third of the spring mass was equal.

Our group had to add 5g to our system to make up for the heavier spring.

First part we had to measure the spring constant which we did by attaching a hanging mass to our spring and measure the acceleration due to gravity and spring constant. We used a motion sensor below the mass to measure its acceleration.

The formula we used was

mg - kx = ma

Our K value was 5.0405

Our mas of our spring is 11g

Here is a picture of our system to measure the spring constant.

Now we used our motion sensor to measure the period of the mass and spring on our system with logger pro. We did this by measure the distance it would travel and the time it would take to go and down.

We repeated this experiment four time increasing the mass. Mass is the mass we had to add to a 100g hanging mass. Period is in seconds

Mass     Period

05g        0.95 s

55g        1.1   s

105g      1.3   s

155g      1.4   s

Next we got the information from the other groups to graph the change of period due to mass and spring constants.

Here is our graph period vs mass which shows as the mass increases the period also increases.

This graph is of only our spring system.

Next is period vs spring constant of the hanging mass 100g and the added mass to make the system equal for all springs. With higher spring constants the smaller the period of the system be.

11/20/2014 Conservation of Linear and Angular Momentum

Purpose:

The purpose of this experiment is to show how linear and angular momentum can be transfered to solve equation involving colosions which produce angular motions.

Experiment:

For this experiement we are going to have a metal ball slide down a ramp and collide into our rotating disk aperateus. We first had to measure the value of inertia for our aperateus which will have the ball colide into to create an angular motion. To do this we took a known mass attached to a string which we then wrapped around our aperateus. Then we used a motion sensosr to find the angular acceleration of the system. We then used the angular acceleration, known hanging mass, known aperateus mass, and the radius where the string wraped around to find the inertia of the aperateus.

Here is the aperateus with the hnaging mass.

Here is our measured angular acceleration:

With our known mass and the average angular acceleration we solved the inertia value of the aperatus shown below.

Know we took the ramp which the ball will roll down on and took measurements of the device so we can determine the height the ball will travel down and then we had to calculate the velocity at which the ball left the ramp.

To calculate the height we just measured the ramp with a meter stick.

To measure the velocity we measured the height of the bottom of the ramp to the floor with a meter stick and took a sheet of carbon paper to mark the landing distance away from the table of the ball.

With that all set up we let the ball roll down the ramp to hit the sheet of carbon paper a couple of times to get the average distance from the end of the ramp to the landing distance on the floor.

With this data we used conservation of energy to calculate the velocity of the ball leaving the ramp.

Here our some measured data we where given for the ball and hanging mass. Also some ramp height measurements are shown.

To the floor from the bottom of the ramp is 95.5cm and the ball landed a length of 52.2 cm from the end of the ramp to the distance parallel to the table top on to the floor.

Here is our energy calculation to find the velocity the ball left the ramp assuming the ball did not slip at all.

Now we had enough information to predict the final angular velocity of the apparatus after collision of the rolling ball down the ramp. Here is our prediction of all the gathered data using conservation of angular momentum.

Finally we performed the experiment measuring the angular velocity of the apparatus after collision.

Here is the apparatus  for collision and our ramp.

Here is our actual values from the experiment which are very close to our prediction.

Actual : 1.775 rad/s

Prediction: 1.95 rad/s