The purpose of this lab is to study projectile motion of an object which is launched horizontally and drops a certain height before it hits the ground.
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This experiment presents an opportunity to study motion in two dimensions. We study projectile motion, which can be described as accelerated motion in the vertical direction and motion at uniform velocity in the horizontal direction. An object launched horizontally with a velocity vx and dropping a height h, has the following relation between its horizontal distance traveled and vx :
You will establish the proportionality constant between the horizontal distance, x, and the horizontal velocity, vx, by studying the motion of a steel ball launched from a ramp.
Sensor Specified In File: | Sensor To Set Up: | Where: | Use: |
---|---|---|---|
✔Photogate | Photogate | DIG1 on LabPro | ✔ |
[If you don’t see the above do the following: Click Experiment→Set Up Sensors→Show All Interfaces→DIG/SONIC1: you can check the photogate by blocking it and seeing “Unblocked’ go to “Blocked”. Click “Close”]
A tool is provided to help you make some calculations from the data in your table. For each mark on the ramp we find the average of the values of t and x using 1.5 from Lab 1 and enter them into Table 2. The error of the average t and x is calculated using expression (1.5b) from Lab 1. The horizontal velocity is then calculated using the formula
and the error in vx is calculated using equation 1.7 from Lab 1.
You don't need to do all these calculations, you just enter your recorded values below and click submit and the calculated values will appear on a new tab. Note that you should enter all distance in meters, not cm.
Copy the values the computer gives you in to the second table in your worksheet. Once you have your values written down you need to make a plot of xavg on the vertical axis (y1,y2,y3,y4,y5) vs vx on the horizontal axis (x1,x2,x3,x4,x5) using the plotting tool below. Should you include the point (0,0) in your fit this time? (Ask yourself what the distance traveled in the x direction is if the horizontal velocity is zero).
We now want to calculate the value of the acceleration due to gravity from the slope of our graph. The slope of our graph, which we will refer to as k, is related to g through equation 3.1, i.e. . We can rewrite this equation as
Now you need to alculate what the value of g should be from the value of k you obtained from the slope of your graph and the value of h you measured earlier. Be careful, if you measured your value of h in cm, you will want to convert it to m so that your value for g has units of m/s2.
Our final task is to estimate the error in our measured value of g. Both h and k have a certain degree of uncertainty and strictly speaking we should take both into account in our estimation of the error in g. You can find the relative error in g from the relative errors in h and k2 using equation 1.7 from Lab 1. The relative error in k2 is obtained from the relative error in k using equation 1.8 of Lab 1. We can then arrive at an expression for the error in g:
Sometimes when we combine relative errors like this we can neglect one of them if it is much smaller than the other. Below there is a tool that calculates the error in g using both the error in h and k, just k, or just h. Enter your values (including your measured value for g, not the official value) and click submit. The computer will display the three error estimates. Based on these three values can you conclude which is the most significant source of error in the experiment? Can you think of ways you could reduce this error?
Finally, you should check whether your measured value of g is consistent with the accepted value of 9.81 m/s2.
When you've done all these things you are ready to discuss your results and conclusions with your TAs.