Forces on a Pulley System

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Kristen Sierman
Lab Report: Experiment #7
Group #4
October 16th, 2012
Forces on a Pulley System
A. Statement of the Problem
The purpose of this lab was to address the following questions: how does the acceleration of a pulley system depend on the mass of the driving objects? And how does the acceleration of a pulley system depend on the mass of the driven object? To achieve this, a dynamic track was set up with a string attached to a cart. The string was part of a pulley system (the pulley was at the end of the track) and connected to a mass hanger, which was vertically suspended. First, the mass of the cart was kept constant (500g) while the weight of the hanger varied (25g, 45g, 65g, 85g, and 100g). In the second part of the experiment, the opposite set-up took place: the mass of the hanger remained the same (25g) while the mass of the cart changed (500g, 750g, 1000g, 1250g, and 1500g). A motion sensor and a computer program called Data Studio were used in each trial to calculate the acceleration. This experiment was done to provide evidence about how mass affects acceleration in a pulley system. B. Prediction

I predicted that the acceleration would not be affected by the mass of the hanger or cart, it would remain the same. My prediction was based on the results of the last experiment (#5), Mass and Motion Down an Incline. In that experiment, it was the angle of the incline, not the mass that affected the acceleration. Hence, I assumed the same thing would happen in this experiment (although there was no incline). C. Data and Results

Mass of cart: mc
Mass of hanger: mH

FAB = mca = T-f(0) → friction is zero in this case
(1) mca = T
(2) FBC = mHa = mHg-T
Add equations (1) and (2) → (mc + mH)a = mHg
(3) a = [mH/(mc + mH)]g
Divide numerator and denominator by mH → [1/(mc/mH)+1]g = a Table (1)
Mass of cart = 500g
Mass of Hanger (mH)| Acceleration|
25g| 0.450 m/s2|
45g| 0.840 m/s2|
65g| 1.540 m/s2|
85g| 1.730...
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