LAB 4

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Indiana University, Bloomington *

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201

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Mechanical Engineering

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Dec 6, 2023

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Jackson Mitton Lab Partner: Eric Cheng Date: 9/28/2023 LAB 4: May the Force be with You. Introduction: This Lab is focused on the different forces acting on an object and how to correctly compute the magnitude of a given force on said object. In the case of this lab, the key object under study is an aluminum block sitting on a balance. There are different types of forces like the normal force of the balance acting on the block, and the reactive force acting on the block as it sits on the balance. But these forces and their values will change as we experiment using a pulley system on the block. Results: Part A Starting with the first experiment that was ran, only one pulley was attached to the object horizontally as displayed in the free body diagram below (figure 1): (Figure 1) The goal was to determine what the frictional force was that kept the block in place under the effect of force pulling it horizontally. If the pulley was not exactly horizontal with the connection point of the block, this could affect the data. For example, if the pulley was higher than the horizon point, it was applying a slight force upwards rather than just horizontally, because it would change the weight read on the scale. By adding more mass to the horizontal pulley, there should not be a change in weight read on the scale because it’s not applying any force vertically. Adding weight to the object itself would change the normal force because the normal force is dependent of the weight or mass of an object acting on a surface. So, increasing the weight of the block (by 10 gram increments) would increase the normal force value by .098 (if the gravity is constant at 9.8 m/s^2) newtons with each new weight. And if the normal force is affected by weight so is the frictional force because more weight would be needed to break frictional force and make the object slide on the surface. However, weight and mass does not affect the coefficient of friction. The recorded weight of the block was: 500.8 grams . Three trials were run for the horizontal tensional force acting on the block before it began to slide: Trial # Total mass pulling horizontally 1 182 grams 2 180 grams 3 180 grams The formula for friction is: F friction = μ s N

Jackson Mitton Lab Partner: Eric Cheng Date: 9/28/2023 So, to calculate the force of friction, we need to calculate the force of horizontal tensional force because it is equal to the frictional force. This would be the average of the values of the three trials (in kilograms) multiplied by the acceleration of gravity: F friction = ( 0.18067 ) × ( 9.8 ) = 1.7705 Newtons . Using this we could calculate the coefficient for static friction by plugging this in and calculating the normal force. F Normal = m×g = ( .5008 ) × ( 9.8 ) = 4.908 Newtons . μ s = F friction F normal = 1.7705 4.908 = 0.3607 Part B The goal of the section of the experiment is to see how the change in the normal force and its vector affect the frictional force acting on an object. Below (Figure 2) is the free body diagram drawn for part B with labelled forces acting on the block: (Figure 2) When 100 grams total are pulling the block vertically that will affect the normal force acted on the block by a degree. Originally as stated before, the blocks exact weight was 500.8 + .05 grams but now the scale read 407.1 grams + .05 grams. Now reusing the normal force equation in part A, we can calculate that the new normal force for the block is (0.4071)*(9.8)= 3.9896 Newtons (scale method). Comparing this to the formula method (theoretical method), we can use this formula to see if the magnitude of the normal force changes or has error: T vertical + F n − mg = 0 . ( .1 ) ( 9.8 ) + F n − ( .5008 ) ( 9.8 ) = 3.92 Newtons So, these two values are almost equal, the only reason that the scale method was higher was due to the fact of a systematic error in which it read 7 grams higher than in the theoretical method. So these two values were expected to be equal or at least very close to being equal to each other because in both contexts, 0 .98 newtons of tensional force was helping the normal force act on the block. We then altered the vertical and horizontal forces pulling on the block to get different values normal forces and tensional forces acting on the block and calculated the normal force, frictional force, and coefficient for static friction: Trial # Tension Vertically (g) Tension Horizontally (g) Calculated Normal force (N) Calculated Frictional Force (N) Calculated Static Friction Coefficient 1 150 128 3.43 1.25 0.364 2 100 162 3.92 1.59 0.406 3 70 160 4.22 1.57 0.372 4 50 180 4.41 1.76 0.399

Jackson Mitton Lab Partner: Eric Cheng Date: 9/28/2023 Part C Now the goal of the last section of the lab was to determine how the frictional force changed when the normal force was applied at an angle that pulled with friction (against the tension horizontally) by setting the vertical tension at a 30 degree angle away from the block and away from the horizontal tension pulley like so:

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