Notebook FV2 - Forces and vectors Ernst

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Iowa State University *

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222

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Physics

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Apr 3, 2024

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Lab FV2 - Forces and vectors Equipment  Metal board with magnetic accessories: o Two pulleys o Force wheel with central floating disk  Set of hangers and masses Important (READ!!!)  To lift and move the magnetic components on the board, always handle the component by the magnetic base.  Magnetic elements that are not in use should be kept stuck to the back of the board Lab FV2 - Page 1

The apparatus The apparatus illustrated below will be used to study the relation between forces in an equilibrium condition. Find the force wheel with the floating disk in the center. Three strings should be already threaded through the center hole. If one or more are missing, please ask your instructor for assistance. Each of the strings should be used to support a hanger with masses as shown. The pulleys have very low friction, so the tension in the strings will be equal to the weight of the hanger + masses. Do NOT use the same masses left and right ( i.e ., do not use a symmetrical setting: it’s a boring one!). Start by placing mass on the center hanger, then add masses to the other hangers and adjust the angles of the strings by moving the pulleys until the disk at the center of the force wheel is more or less “floating”. Finally, lift the force wheel gently off the board and move it on the board as needed until the floating disk is perfectly centered with the force wheel. In this position, the disk is, indeed, floating: it is not in contact with the wheel. If we neglect the weight of the disk (which is indeed very small), the only forces acting on it are the three tensions in the strings. Lab FV2 - Page 2

Prelab review: components of forces and propagation of uncertainty For this activity, we will concentrate on one of the forces: the tension in the top, right string, indicated as T 1 in the figure below. What is the magnitude of T 1 in your setup? Don’t forget to take into account the mass of the blue hanger! T 1 = 0.115 * 9.8= 1.128 N Forces are vectors, and so we need to work with their components. Write the components of T 1 for the coordinate axes shown in the figure, in terms of the magnitude T 1 and the angle θ 1 . (This should be an algebraic expression, do not use numerical values yet.) T 1,x = T 1 * Cos( θ ) T 1y = T 1 * Sin ( θ ) To measure the angle with ease, the dial of the force wheel can be rotated to align the 0° mark with + x direction. If your x axis is horizontal, the bubble level will be helpful. What is the value of θ 1 in your setup? 28 Lab FV2 - Page 3

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Use the measured value of T 1 and θ 1 to calculate the numerical value of the components of . x=0.996N y=0.530N Uncertainty However, no measurement is perfect! The masses we are using have an uncertainty of  2% around their nominal value. A reasonable estimation of the uncertainty in the angles could be set to  1° (we can read the angle with a precision of about 0.5°, but we are increasing it to account for the friction in the system, which results in a certain variation in the position of the strings in equilibrium). Rewrite the values of your experimental values for T 1 and θ 1 , including uncertainty: T 1 =1.128 N  0.223N θ 1 =28°  1° Uncertainty is propagated through any calculation. Rewrite the components of including uncertainty. (This is what you did in the prelab.) On paper Lab FV2 - Page 4

Experimental setup and background Let us go back to the whole system. The figure below shows the free-body diagram for the floating disk. (The mass of the disk is negligible.) The disk is in equilibrium. Therefore, according to Newton’s laws: [Equation 1] The magnitudes of these forces are equal to the hanging weights: Let us now rewrite vector equation [1] in terms of components, using the coordinate system in the figure. [Equation 2] Lab FV2 - Page 5

Data collection Check that your setup is not symmetric (i.e., m 1  m 2 ). Record the values of m 1 , m 2 and m 3 (remember: they must include the mass of the hanger!) and the angles  1 and  2 . m 1 =0.115kg m 2 =0.105kg and m 3 =0.107kg  1 =28° and  2 =19° Data analysis Our goal is to experimentally verify the relations in equation 2. However, chances are that when you compute, say, the two x components, and add them (first line in equation 2), the result won’t be exactly zero. This does not mean that Newton’s Laws are being violated! Every measurement has an uncertainty, and and we need to propagate it through every step of the calculation: 1. When you calculate of the magnitude of the forces 2. When you calculate each component for every force 3. When you add the components in equation 2. Steps 1 and 2 were done in the Review section above. This needs to be done for each force! Your final result should be something like this: In the example above, would you conclude that equations 2 are verified within the uncertainty of the experiment? Explain. For the net force of x, the range is from -4 to 2 so 0 is in between that so it does work, it needs to equal 0 because equation 2 says the forces equal 0, but the y axis is from 1 to 9 so 0 is not between so the y equation does not work. Time to analyze your own data. Show all your calculations. (We recommend doing them on paper and inserting GOOD photographs.) Initial uncertainties:  2% for masses,  1° for angles. Lab FV2 - Page 6

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Conclusions Does your data verify Newton’s second law, i.e. , equation 2? Your reasoning must include uncertainty. It did work for us because we got the same number within the uncertainty. Our X net was 0.022 +- 0.038 so it can be equal to zero which is what the second equation says. Our y net doesn’t equal zero but it does fall into the equation above when it equals 1. Lab FV2 - Page 10

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