15-March-2017: Lab 5 -- Trajectories

Eric Chong

Lab 5 -- Trajectories

Lab Partners: Lynel Ornedo and Harvey Thai

Purpose: To use your understanding of projectile motion to predict the impact point of a ball on an inclined board.

Introduction/Theory: Objects in a projectile motion are subject to changes in their x and y components of velocity and position, be it due to air resistance, gravity, inertia, etc. Each component is independent of each other and should be solved individually. The variable that connects the two components is time. Since the time it takes for both the moment when the y-component reaches the height of a certain position and when the x-component reaches the distance of the selected position from the point of origin are the same, the value for time can be applied to both x and y properties of the object. By solving for the time an object reaches a certain point using the kinematic formulas, we can use the time to find the velocity and position values of the object, and even predict the impact point of a ball on an inclined board.

Procedure: Professor gave us a page with all of the procedures we need. Here is a picture of the procedure and the pictures of the apparatus with two parts, one without the inclined slope and one with the inclined slope:

Part 1) For part 1 of the lab, we first found the initial velocity when the ball started shooting off of the edge of the table. To do this, we measured the height of the table to the ground and found it to be 0.947 m. We then identified approximately the distance at which the ball hits the ground from the foot of the table and taped a piece of carbon paper at the location so we could physically measure the distance that the ball marked. We launched the ball 5 times and measured the average of those 5 trials. We ended up with around 0.709 m for the distance traveled. In our calculations, we found the time it takes the ball to land, and then we used that time to find the initial velocity of the calculation. Here are the results and the calculations to find the initial velocity:

The results came out to be 1.612 +/- 0.002 m/s.

Part 2) For part 2 of the lab, we have to find the distance on the inclined board the ball would hit. To calculate this, we first derived an equation that would calculate the distance on the board the ball would hit based on the ball's initial velocity. Here is the derivation, where d is the distance on the inclined board:

Now that we have this derivation, we can measure the angle the incline and plug in the value of velocity we got from part 1 of the lab and the angle to get the distance on the ramp the ball would hit. We measured the angle of the incline to be 50 degrees. Here is the calculation:

Of course we must calculate the uncertainty in that measurement as well. The uncertainty in the angle is +/- 0.1 degree, and the uncertainty in the initial velocity is +/- 0.002 m/s. Here is the calculation:

Notice that I did not use the "square root form" when calculating the uncertainty, and both ways are fine. The result with the uncertainty turned out to be 0.982 +/- 0.319 m. When we actually launched the ball, the ball actually hit between 0.942 m and 1.003 m down the ramp. The theoretical result and the experimental result turned out to be accurate.

Conclusion: During this lab,  I mentioned that there may be uncertainties in the experiment. The biggest error came from possibly the inertia of the ball. The ball itself has some mass, and that mass might affect the inertia to the point of it being not negligible. Some other sources of uncertainty might be the placement of the ramp, as the angle measured might not be accurate. Our device for measuring the angle is also not appropriate for a lab setting, as we used a phone app to measure it, rather than using a protractor. And another uncertainty, though this may be negligible, is the air resistance. Another source of uncertainty that may affect the data could be the friction on the ramp. We were unsure whether the ramp was completely frictionless when the ball was rolling on it and off of the edge of the table. This could affect the initial speed and and ruin our calculations. These are some of the more obvious sources of uncertainty that we came up with.

Overall, this lab taught us the mechanics of how projectile motion problems work by having us calculate the motion of a ball in the air and where it lands.Gravity affects only the y-component of the ball, whereas the x-component is unaffected, unless stated otherwise. By calculating the time, we can slowly calculate each individual velocity and position components of the projectile.