Slope - All linear fits have a constant slope, and in this case the slope=1.190 m/s/s. This is clearly a linear fit, which means that Acceleration is directly proportional to ∑F.Įquation - Acceleration = 1.190m/s/s/N * ∑F -0.1078m/s/s #5 Repeat step #3 to #4 for different hanging masses #4 Record the acceleration by calculating the slope of the resulting Velocity V.S. #3 Record the total mass of the hanger (or net force) and release the cart from rest while the motion sensor is collecting data #2 Connect a motion sensor to LoggerPro to collect motion data (Velocity V.S. #1 Measure the mass of our system (cart, string hanger, all of the hanging masses, etc.) We will change the net force by MOVING mass from the cart to the hanger instead of ADDING them. The more mass an object has, the more inertia it has and the more resistance to change in motion (acceleration) it has. Why do we have to keep the total mass constant? How do we do this properly? Independent Variable - the NET FORCEacting on the systemĬontrols - TOTAL MASS of the system, other parts of the system including the hanger, the track and the cart Research Question - What effect does changing the NET FORCE on a system have on the acceleration of the system? The simulation below shows one vector decomposed into its x and y components.Experiment 1 - Net Force and Acceleration If we have an x-y coordinate axis, any vector on this axis can be decomposed into its x and y components. Our mathematical framework for dealing with multiple vectors involves using vector components. Does it differ from the analytically derived slope by less than the uncertainty? There are more details about this process here. $$\textrm$$įind the slope of your linear data and compare it to what the slope should be from your analytical equation. Plot the results (both experimental and anlytical) with the mass of $P_3$ on the vertical axis, and the $\cos(b)$ on the horizontal axis. We can make the data a little easier to work with by plotting the mass as function of the $\cos(b)$ instead. Your plots should like a section of a cosine function. On one graph plot the experimental data from your table along with the analytical prediction of the function you found. In the box below, enter the formula you have found that will predict the mass of Pan 3. It should be something of the form $P_3 = C \cos(b)$, where $C$ is a constant. Using some basic trigonometry, determine an equation that we can use to predict the mass of $P_3$ as a function of the angle $b$, and the mass of $P_1 P_2$ (considered a constant equal to 200g). We would expect there to be some mathematical relation between the angle $b$, the mass of $P_1$ and $P_2$, and the mass of $P_3$ needed to balance the system.
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