AP Physics: Cart Experiment

1. Mar 30, 2015

Bayuki

For this experiment, students must be able to find the acceleration of a cart using kinematics, dynamics, and energy. A cart with a mass on it (mc=2.48kg) is connected to a mass-less string which is connected to a pulley (mp=0.004kg). A hanging mass (0.02kg) is also connected to the pulley. I tried the kinematics route of solving for the acceleration and I got a=(2Δx)/t2. Also, since our tables weren't high enough, we couldn't use the time for the entire cart to get to the pulley. Instead, we stopped the cart at 0.64m (which would be x) from the starting point. The time we got was 2.73s to get to 0.64m from the starting point. So using the equation I previously stated, I got 0.17m/s^2 to be my acceleration. Can someone check if my work is correct or if my equation is used correctly?

Aside from kinematics, we had to use dynamics and energy. We also did dynamics in class today. I made three free body diagrams (in the paper from class), with the cart having FG down, FN up, and FT to the right. The hanging mass has FG down and FT up. Also, my teacher said that there must be a free body diagram for the pulley because it is rotating and taking acceleration. So the free body diagram for the pulley was FT down, FG down and FN up from the center (not in the image uploaded), and with a torque going clockwise with an acceleration of α. So far, what I have tried doing is finding the FT. I got Ft= M(cart)g - ma and Ft=m(hanging mass)a. So then I made both FTs equal to each other and got Mg - Ma = ma. Obviously I've got no clue as to what I'm doing at this point considering I ended up solving for acceleration instead of FT. I still have no idea where the pulley plays into all of this. Can someone lead me in the right direction?

I also needed some help with finding acceleration using energy, and even though I haven't tried it yet, I don't know where to start ...

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Last edited: Mar 30, 2015
2. Mar 30, 2015

Staff: Mentor

Welcome to the PF.

Can you try scanning your page or somehow posting a cleared-up vertical image? It's pretty much unreadable for me.

As to the pulley, have you covered Moment of Inertia (MOI) yet in class? You will need that to help you with your torque & angular acceleration part of this problem.

3. Mar 30, 2015

Bayuki

Unfortunately all I could do is make it vertical. The actual paper is not with me so I can't scan it for a sharper image. Sorry.

As for moment of inertia, yes. We have gone over that earlier in the year (I wanna say mid to late December?). We are now reviewing for the AP Physics 1 exam which will be in the first week of March. The pulley is a solid disk, so I=1/2MR^2. However, how would I tie that in with the other two (the cart and the hanging mass)? I recall some sort of equation that went like A(total)=√ac2 + at2, with ac being centripetal acceleration and at being transitional. Would this be something I would use?

Thanks a lot, berke.