Motion Down a Ramp

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University of Minnesota-Twin Cities *

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Physics

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Feb 20, 2024

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Motion Down a Ramp - Exploration, Measurement & Analysis Exploration Try a variety of different track angles, release heights, and cart masses to determine the combination for which the cart moves smoothly in a controlled manner. Determine what range of these quantities you can use for your measurement. ❖ For us we found: Placing one wooden block (8.4 cm tall, the release height) to determine the combination for which the cart moves smoothly in a controlled manner. ❖ The angle being =4.725° ❖ Adding the weight makes the car at this angle go down slower compared to a higher slope. Why is it important to click on the same point on the cart in each frame to record its position? ❖ It’s important to click on the same point on the cart in each frame to record its position because that’ll allow us to get the most accurate measurements depending on the angle from which we measure. If we were to click different points from the cart, then our numbers wouldn’t correlate with each other. How will you increase your ability to do this? Estimate your uncertainty for clicking on the same point in each frame. ❖ We will increase our ability by clicking on the same point in each frame per second to be able to fully calculate each point of velocity the toy car travels at. What quantities in your prediction equation can be measured with the video analysis software, what quantities are best measured without the video, and what quantities must be calculated from the video data? ❖ The quantities in our prediction equation that can be measured with the video analysis software are speed, velocity, distance. ❖ The quantities that are best measured without the video are distance, and angles. ❖ The quantities that must be calculated from the video data are time and speed. Measurement Time Distance Angle Sin Θ=

2.20 s 178 cm Θ=4.73° h=8.4cm 4.72 = 46. 25 cm/s^2 1.66 s 178 cm Θ=10.01° h=18.1cm 10.17= 99.65 cm/s^2 1.40 s 178 cm Θ=14.91° h=26.5 cm 14.89 = 145.90 cm/s^2 Mass of cart staying the same at 252.2g Sin a= b/c Acceleration (sin a= h/d): 32 cm/s^2 Velocity (sqrt (2gdsina) = sqrt (2gh) Position vs. Time Graph (1.66 s) Velocity vs. Time Graph Position vs. Time Graph (1.40 s)

Velocity vs. Time Graph Position vs. Time Graph (2.20 s) Velocity vs. Time Graph

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Analysis How can you estimate the values of the constants of each function from the graph? ❖ We can estimate the values of the constants from the calculated functions of each point made as the cart accelerates. Use your data to determine the speed of the cart at the bottom of the track just before it hits the stop ❖ The speed of the cart at the bottom just before it hits the stop is 120.23 cm/s^2 Make a graph that compares the final velocity of your cart and the ramp's angle for your prediction and measured data. Use the same data to graph the cart's final speed versus the ramp's height. Which graph would be easier to use? ❖ The graph that is the easiest to use is the one with fewer points because those points are the ones that matter the most. Look at your graphs and rewrite all of the fit equations in a table, replacing the computer generated labels with the appropriate meaningful quantities. If you have constant values, assign them the correct units and explain their meaning. ❖ x(cm) vs. t(s) - is position (distance) the car has moved vs the time (how long it look) to get to the bottom ❖ v(cm/s) - is the final velocity of the cart in cm/s Why are there fewer data points for the velocity vs. time graphs compared to the position vs. time graphs? ❖ There are fewer points in the velocity vs time graph because it is linear, whereas the position vs time graph is a polynomial graph. Is it constant as the cart goes down the ramp? Explain why it should or should not be constant using your knowledge of interactions. ❖ It shouldn't be, because it isn't moving on a flat surface. It is moving down a ramp, making the gravity pull the force down.

Are your video analysis measurements close to your stopwatch and meter stick measurements? If not, which ones do you trust? ❖ Our measurements are very close to our stopwatch measurements towards the middle of the chart. This is valid because they both include the same numbers (time and distance). As it isn't the exact and still a little off I would trust the computers numbers more because my reaction to start and stopping the time is different then when it actually stops (reaction time).

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