Friction Forces

Purpose:

In this lab, the main purpose to determine the static friction between the block and table top. To do so,  we need to get the block at the breaking point to sliding. We measured the static friction 4 different methods. Water cup, slope force sensor, force sensor pulling, and weighted mass. 

Lab Set Up:

Here we used a force sensor on a sloped surface. We let the block slide down from a certain length and measure the acceleration. 

Here we used the mass at the end and force sensor to measure the force of the block.  As the mass increases, the acceleration also increase. 

Another method we used is the water cup. We attached a water styrofoam cup to one end and tied the other end of the block. For the first block, we filled the cup slowly with water until the cup starts to slip. Then we measure the mass of the cup and record the weight. We repeat this process with 2, 3, and 4 blocks. 

This data table is for the water cup method.

The maximum static friction is the slope of the graph. Here the slope is 0.3649.

Force Sensor Pulling Method. As the block increase the average kinetic friction doubles. 

This is the slope of the ramp which we set up. 

Summary:

In this lab, we discover the many different ways to test and calculate static and kinetic friction. The most accurate is the force sensor method. To obtain the coefficient of friction, we must plug in the value in a chart and test a linear fit to find the slope. 

Unknown Mass Lab

Purpose:

Using what we know about springs, we have to calculate what is the unknown hanging mass and propagate the uncertainty.

Lab Set Up:

The apparatus was already setup by the professor. Spring 1 is the top left and Spring 2 is the top right. Here we measure the spring's forces and angle to determine the unknown mass.

In this setup, we only take account for the y components because the x components has no effects. We set the sum of y components equal to mg and solve for mass. For the uncertainty, we used the known uncertainties from the springs and protractor. 

This is the equation we used to determine the uncertainties.

This the uncertainty for the unknown mass. We plugged in the measured values into the equation and solved. 

For our unknown mass, we calculated a value of 0.531± 0.8kg. The value seems reasonably accurate.  The photo below is our work for the mass. 

Summary:

In this lab, we measured the forces from each spring and the angles. From there we setup a net force equation equal to mg and solved for mass. For uncertainty, we took the derivative for each measured valued. 

9-Sep-2014: Projectile Motion

Purpose:

The main purpose of this lab is to first come up with an equation to determine the distance of the impact point of the ball by using the known measurements (i.e. height of the table, height from floor to release point, and angles).

Lab Set Up:

Top part of the apparatus. Equipments used were two v-channels, two wood blocks, clamps, board, steel ball, and carbon paper. We used a pencil to mark the location where the steel ball was released.  

The carbon paper was taped onto the board because the impact of the steel ball will mark the paper indicating the distance.

In order to determine the distance of impact, we had to record a few measurements. The measurement recorded were, height of the ball, angle of the board, and height of the table. 

This is the equation that was derived to determine the distance of impact.

Using the equation we determined, the distance calculated was 0.774m. The photo on the bottom is the calculation with the values plugged in. 

Summary:

We setup our apparatus as shown in the lab handout, then we measure the needed measurements to obtain our unknowns. With the values measured, first we were able to calculate the time and velocity. Then with those values, we plugged in the equation for distance. Our model matched our experiment, so therefore our model was accurate. 

4-Sep-2014: Measuring the density of metal cylinders

Purpose:

The main purpose of this lab is to measure the density of the metal cylinder using calipers and micrometer. Along to measuring the density, we will propagate the uncertainty of our calculations.

Lab Set Up:

The picture below is the caliper we used to measure the metal cylinder. The calipers have an uncertainty of about 0.01 to 0.02 cm. We used the calipers to measure the height and diameter. We obtain the value of 1.42 ± 0.02cm for the diameter. For height, our value were 5.08 ± 0.01cm. 

 The picture below is the scale that was used to weigh the metal cylinder to determine the mass. The scale has an uncertainty of 0.1g. Our value for the mass was 62.1 ±0.01g.

Procedure:

Using the calipers, measure the diameter and height of the cylinder. Using the scale, weigh the cylinder to determine the mass. Be sure to obtain the uncertainty of each devices used. Since we have the value for the diameter, height and mass, we could measure the density. We used the equation density = mass/volume and volume = height * pi * (radius)^2. Also for the uncertainty we used to the standard deviation equation.

Data/Calculation:

In the following pictures, it shows our calculation for the density and uncertainty. 

The density for this metal cylinder is 7.49 ± 0.26g/cm^3. 

The density of this metal cylinder is 17.5 ± 0.404 g/cm^3. 

The density of this metal cylinder is 8.005 ± 0.719 g/cm^3. 

Summary:

In this lab, we measured the values for height, diameter and mass, to determine the density. We also calculated the uncertainty of our density based on the equipments used. 

28-Aug-2014: Free Fall Lab

Purpose:

Our purpose in this lab is to prove that gravity is 9.8 and a free fall object has an acceleration of 9.8m/s.

Lab Setup

 The apparatus above was used to mark the spark sensitive tape as the object is free falling.

This spark sensitive tape shows the distance the object was at a time. This data could be used to obtain a Distance vs Time Graph and Velocity vs Time Graph. 

Procedure:

1). First we align the spark sensitive tape with a meter stick and recorded the distance where each spark was marked. (Tip: align the 0 cm mark with the first dot then record your data from there)

2). Next, open a new excel worksheet. Column A is Time, Column B is Distance, Column is change in distance, Column D is Mid-interval Time, and Column E is Mid-interval Speed.

3). The first data point across is 0 because that is the starting point. Except of Mid-interval time, enter A2+1/120.

4). Enter the rest of the data including the distance and time. The time interval would be 1/60.

Data:

Below is a screenshot of our data table and graphs. Time vs Distance is a exponential fit and Mid-interval Speed vs Mid-interval Time is a linear fit. These data points are valid because they show that the accelerating is very close 9.8m/s. 

Summary:

We measure gravity by using the an apparatus that generates sparks and marks the position of the object as it free falls. Using the data collected from the spark sensitive tape, we were able to prove that gravity for a free falling object is 9.8m/s by plugging in our data into excel to find a fit for our graphs. 

26-Aug-2014: Inertial Balance Lab

Purpose:

In this lab, our purpose is to determine the relationship between the mass and period for an inertial balance. We are determining an equation to connect the mass and period for an inertial balance.

Lab Setup:

 Here we used a clamp to hold the inertial balance to the table. We place the photogate at the other end of the inertial balance to record the period. 

Here we use tape to safely secure weight to the end near the photogate. We then pull the balance to create a period which the photo gate will record.

Description:

In this lab, we are recording the period of the inertial balance when it is empty and when weights are slowly added on. To do so, we must find the average period with no additional weights, then add 100g and find the average period. We repeat this until we reach 800g. With the equation we come up with, we will be able to determine the mass of our unknown by simply using our average period. The photogate is connected to our LabPro which is connected to our Macs. 

Data Table:

Our Mtray range is between 320g-350g. With these values, we were able to get 0.9997 for our correlation. We plotted a period vs mass and it was a linear graph. 

This is our calculations. To find the mass of the unknown. We used Ln(T)=n*ln(Mtray + m) + lnA. 

Summary:

We came up with an equation that is very precise. We developed an equation with our obtain period values and known mass.