18-Sept-2014 Friction Lab

Purpose:
To calculate the coefficient of static and kinetic friction between the table and the wood blocks.

12-Sept-2014 Determination of unknown mass.

Measuring the Density of Metal Cylinders

Purpose for this experiment was to learn how to calculate propagated uncertainty.

Here we are measuring the density of 3 metal cylinders. With the use of calipers we measured the diameter and height. Calipers can have an error of (+/-) .01cm. Mass was measured on a scale with error of (+/-) 1g.

density = (4*m)/(h*pi*D^2)

Determination of an unknown mass

My table decided to look at unknown mass #10. 

uncertainty of angle = (+/-) 2 degrees

uncertainty of force = (+/-) .5N

m = .704kg

uncertainty of mass = .9%

09-Sept-2014 Trajectories

In this lab we will be using our understanding of projectile motion to predict the impact point of a ball on an inclined plane.

So for part 1, easy as cake, we figure out time using the equation with initial velocity equal to zero and acceleration equal to earth's gravity:

∆y = vt + (1/2)gt^2 = (1/2)gt^2

t = √(2∆y/g)

Using time, t, and the horizontal displacement, ∆x, we can calculate the ball's initial horizontal velocity:

∆x = vt

Now for the second part we modify the equation because the ball is now landing above ground level onto an inclined plane. 

∆x = dcos∂ = vt

t = (dcos∂)/(v)

∆y = dsin∂ = (1/2)gt^2

d = (gt^2)/(2dsin∂)

d = [(v^2)2sin∂]/[(g)cos^2(∂)]

As seen below, my calculated/predicted landing point on the inclined plane was .4647 m. The actual point of landing was .47 m. I was off by -1.12%. This error could have been from the meter stick or from the angle finder, both of which rely on my vision.

04-Sept-2014 Air resistance lab

The purpose of this experiment is to determine the relationship between the force of air resistance and speed of a falling object.

For the setup we used a lap top, camera, meter stick, coffee filters, and the second story balcony of building 13. The camera and laptop were positioned above ground level at a point equadiastant from the release point and the landing point. 

For the first round a single filter was dropped and recorded on video. Then two were stacked on each other and dropped. We continued this until the fifth round where a stack of five were dropped. In doing this we can determine the terminal velocity of the coffee filters.

The data was collected using the video function of LoggerPro to follow the position of the filters vs the time.

From the position vs time graphs the terminal velocity can be acquired for each of the drops. This is where the graph no longer curves and seems to remain constant. Then we use velocity, v the equation:
        F(of resistance) = kv^n
        k = 0.008542
        n = 1.794
        m(of 1 filter) = 1.035 g

28-Aug-2014 Free Fall Lab

We have been told that in the absence of all other external forces except gravity, a falling object will accelerate at 9.8 m/s^2 and the purpose for this experiment is to prove that.

The device we used is pictured below. It is said to be 1.5 m high and consists of a powered electromagnet at the top. From top to bottom along the device's body there is a wire which is connected to a spark generator. This will emit a spark, at a constant time interval, as a metal plumb bob falls from the electromagnet. Between the path of the falling plumb bob and the sparking wire a strip of  spark-sensitive paper is placed so that every time a spark is generated, a mark is left behind.

We have conducted the experiment at this point and the parks have been collected on the strip of paper. In terms of time each of the spaces are equal, 1/60 second, but this is not the case for the physical distance between each mark. So what we do now is measure as accurately as possible the space between each of the marks as they increase.

The time and displacement were then put into a chart on excel so that we could use them to find the graphs of position vs time and velocity vs time. We can see that the position vs time graph curves which confirms that velocity is changing, increasing in this case. The velocity vs time graph was then plotted and what we got was a linear graph which confirms a constant acceleration. Our acceleration was measured to be 9.38 m/s^2 and although our constant acceleration was not exactly what we were looking for it is what we measured.

Average velocity was calculated using the equation:
        v = [x(b)-x(a)] / (1/60)
where
        t = [a,b]
The overall class average for acceleration was 9.48 m/s^2.



So why the wrong "answer"?

It's not so much a calculated error but instead an experimental uncertainty. For one, the calibration in the meter stick is not great but rather "good enough" for most things. So how wrong were we?
        Relative difference = [(9.48-9.8) / (9.8)] * 100 = -3.26%

28-Aug-2014: Power law for an inertial balance.

The purpose for this experiment was to find a relationship between mass, of any object, and period for an inertial balance.

Below is the setup of the experiment. We started by clamping an inertial balance, a spring device which oscillates (side to side in this case), to the table top. At the outer end of the balance we placed a piece of tape. The piece of tape was adjusted so that it would pass through a photogate. Every oscillation cuts an invisible beam and after two full oscillations a period, length of time, is counted then recorded into Logger Pro on the lap tops.

Below you can see the data table where I wrote down the measured period for each of the different masses that were added to the end of the inertial balance. As we can see there seems to be a correlation between mass period but why has the larger mass resulted in longer period? Mass was recorded in grams and period in seconds.

The masses were converted to kilograms and the data was then plotted on a graph that resembled the standard linear graph of:

y = mx + b 

Our original equation looked like this:

T = (M+m)^n + A

Where M is the mass of the tray, and m is the known mass placed at the end. We then have our equation a bit of a modification in order to make it more pleasing to the eyes. We did so by taking the natural log of the whole equation and obtained:

lnT = (n)ln(M+m) + lnA

        Mass of the metal weights, M: KNOWN

        Mass of the tray: UNKNOWN

        Slope of the graph, n: KNOWN

        The y-intercept of the graph, lnA: KNOWN
        The y components, lnT or ln(period): KNOWN
        

Below you can see the chart I made where I included the known parts and included the correlation, which tells us how well the line and points fit together. We then tweaked the value of n to find a low and high value for M that would give us .9999 correlation.

        M low: 350g              M high: 440g

        lnA low: -0.4582        lnA high: -0.5273

        n low: -0.7163            n high: 0.8066

Finally, assuming that we ran the experiment correctly and collected the proper values we should be able to return to our equation of:

lnT = (n)ln(M+m) + lnA

and use it to calculate a very close approximation of an unknown mass at the end of the inertial balance. Below is an other table where I ran the experiment all over again using a laptop charger and a wooden block, both of unknown mass, and wrote down the period, T, of each.

        Mass of charger: unkown        Mass of wood block: unknown

        T = .432 seconds                    T = .401 seconds

Using the data from the previous two tables we can calculate a range for the unknown masses, which I've done below. 

From all of this we are able to derive a fairly accurate power law.