Constant Forces and Motion Questions

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Feb 20, 2024

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Constant Forces and Motion We had a cart on a flat plane attached to a weight on a string through a pulley for the experiment. We conducted four trials with different weights so that the ratio of the cart to the hanging mass varies. (hanging mass/cart weight) = ratio Trial 1: (50 g / 256.4 g) = 0.196 Trial 2: (90 g / 256.4 g) = 0.351 Trial 3: (130 g / 256.4 g) = 0.507 Trial 4: (170 g / 256.4 g) = 0.663 Make plots of position and velocity -- do you recall how to find velocity from position vs time plots? -- for each of these trials. Velocity is the derivative of position/time so the slope of the plot would be the velocity. Determine the cart's acceleration (and its uncertainty) while the hanging object is still falling (is it better to use the position vs time or velocity vs time plot here?), The velocity vs. time plot would be better to use to determine the cart’s acceleration since acceleration is the derivative of velocity/time. It is simpler to use that plot rather than using position vs time and finding the second derivative to find the acceleration. And the cart's velocity (and its uncertainty) after the hanging object hits the floor (again, is it better to use the position vs time of or the velocity vs time plot here to find this?). It would be easier to use the velocity vs time plot to find the velocity at a certain time since we’d have to find the derivative/rate of change for the time we want versus plugging into the equation. Does the velocity of the cart change after the hanging object hits the floor? After the hanging object hits the floor, the velocity of the cart stays constant.

Can you find some relation between the acceleration of the cart, its final velocity, and the distance the hanging object has fallen? Is this consistent with your data? Repeat for all trials. The distance for all of the hanging objects are all the same as we kept the cart at the same position each time. The final velocity for all of the trials except the 1st one was -1.5 m/s. It could be a coincidence but three of the data aligned and The gravity acted upon the hanging object pulls the cart towards it thus if the mass of the hanging object increases, the acceleration also increases as both the mass and the gravity acting upon it is pulling the cart. And if the velocity/acceleration higher than the distance that it travels will also increase. Applying Newton's second law to this system, as you did so in the pre-lab, one can find a relationship between the acceleration of the system and the ratio of mass of the hanging object to that of the cart. Plot the experimentally-found accelerations as a function of the ratio of the mass of the hanging object to that of the cart mass. Does it form a straight line? The line of the acceleration vs ratio plot fits a polynomial line more than the linear. More importantly, should it form a straight line?! If not, think about why considering what you found, using Newton's 2nd law, for the acceleration as a function of these masses. I don’t know to be honest. Newton’s Second Law is F=m/a. What should the slope of the plot of the experimental data be when this ratio is small (when the mass of the hanging object is much less than that of the cart)? If the ratio is small, then the slope of the position vs. time graph would be less steep than the slope of a greater ratio. The slope of the velocity vs time graph would be less steep as the acceleration is smaller than if the ratio were larger.

Are your experimental results consistent with this? Yes. What should the slope of this plot be when this ratio is large, and, hence, what is the limiting value of the acceleration when this ratio is large (when the mass of the hanging object is much larger than the mass of the cart)? Does this make physical sense? Do your data agree with this trend? The slope will flatten out quicker since the acceleration will be larger so it will hit the ground quickly meaning the velocity will become constant afterwards. Yes our data supports this trend.

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