Note Feb 13, 2025

LAB 2 Forces And Accelerations In this laboratory, we will be analyzing a spring scale and a cart and track system with a various assortment of masses. The goal of this lab is to better familiarize you with Newton’s Laws as well as forces and accelerations in general. Given Quantities • Track Length = 0.8m • Mass of Weight Hook = 5g • Mass of Cart = 520g • Mass of Pulley = 30g • Mass of String º 0.5g • Mass of Rectangular Metal Block = 500g 2.1 Analyzing Net Force And Accelerations In this part of the lab, we will try to better understand the relationship between forces and accelerations by using a mass and a spring scale. As background, a spring scale works in a similar fashion to an ordinary household scale. When a weight is attached to it, its spring stretches and the scale displays the weight of the attached object in units of Newtons. Figure 2.1: 500 Gram Mass on Spring 105

2. F ORCES A ND A CCELERATIONS 1. Take the 500g mass (or another mass that you have been provided) and attach it to the end of the spring scale. Because the spring scales may not be totally accurate, record the reading on the scale in the space below. 2. Draw a Free Body Diagram for the mass and spring scale system while it is at rest in the space below. Include the “Force of the Scale” and “Weight of the Mass”. Indicate the relationship between these two forces. Figure 2.2: Moving Scale 3. Before we proceed any farther, let’s do a quick thought experiment. What would happen to the reading of the scale if you were to move the scale up or down with a constant velocity, while the mass was attached (but without touching the mass)? Would the reading on the scale increase, decrease, or stay the same? Briefly explain your reasoning. 4. Now, with the 500g mass attached, hold the scale and move it up and then down with a constant velocity. What happens to the reading of the scale as you do so? Was your group’s hypothesis correct? If not, explain why. 5. Draw a Free Body Diagram for the mass and scale system as it is moved with constant velocity. Indicate the relationship between the “Force of the Scale” and “Weight of the Mass” and indicate the direction of acceleration if applicable. 6. Before we proceed any farther, let’s do another quick thought experiment. What would happen to the reading of the scale if you were to move the scale up from the floor to approximately shoulder level rather quickly? Would the reading on the scale increase, decrease, or stay the same? Briefly explain your reasoning. 7. With the 500g mass attached, one teammate will hold the scale (with mass still attached) close to the ground and then move it up to shoulder level rather quickly. The rest of the team will observe the reading of the scale. What happens to the reading of the scale as the mass is moved quickly upward? Was your group’s hypothesis correct? If not, explain why. 106 5009 f e The force of the scale and the weight of the mass are pointing in opposite directionscancel out each other The mass reading should stay the same becamethe same forces are atting on the mass canceling eachother out no newforces Our hypothesis was robbed The wedding stayed the same because nonen forces were intruddled t ff ff fff ff Had the Mouth The reading on the scale will increase The all elevation caused by mouns the system quickly will allow the magnitude of the spring truce tobe greater than the magnitude ofthe gravitational force Our hypothesis was correct The reading increased This is neat tiara a'facilitate is 88

2. F ORCES A ND A CCELERATIONS 2.2 Newton’s First Law / Analyzing Simple Accelerations Take your track and place it flat against the table, and then place your cart on the track. Ensure that the track is flat and level, and that the cart can remain at rest while on the track. Adjust the track as necessary. Ensure that the “Bubble Level” is securely attached to the cart using the piece of putty, and that the bubble is centered between the lines when the cart is at rest i.e. that the level is parallel to the table. Assume that all surfaces are perfectly smooth, which means the cart does not slow down due to friction. Refer to the picture below. Figure 2.3: Cart on Level Track 1. Briefly explain Newton’s First Law and provide an every-day example below. 2. Before we begin the next part of the lab, let us briefly think about what is inside of a bubble level. Consider that a bubble level contains some sort of fluid, and some sort of gas. For our purposes, we can assume that the level contains a combination of water and air. Which of these components likely has more mass, the water or the air bubble? Now we are going to try and make some predictions. For each of the motions described below, predict where the bubble will be in the level and sketch the location of the bubble within each box. For each case, try and briefly explain your prediction. It may also be helpful to think about what happens to the fluid that is in the level during these time periods. Case 1: Cart moves to the right and is speeding up. Case 2: Cart moves to the right with constant velocity. Case 3: Cart moves to the right and is slowing down. Explanation: Explanation: Explanation: Now you will try it out. Take your cart and place it at the end of the track farthest away from the bumper. With your hand, give the cart a gentle but quick tap toward the end of the track with the bumper. 1. While your hand is pushing the cart, sketch the position of the bubble. What can you say about the cart’s 108 An obielt initially at best remains at best an d obielt initially in motion remains in lineau motion constant velocityunless it alted on by a nonzero wet tone A toytoo well stayin place until you push It down the table the wa Fmoremasssu heaiunubbleiantoatandtfitmning.is level or not The bubble my stanninesame EE iiiEii.iaa If iii on n is nYii aains on it

2.2. Newton’s First Law / Analyzing Simple Accelerations acceleration during this time, is it zero or nonzero? Draw a Free Body Diagram of the cart at this time and if applicable, draw an arrow that points in the direction of the cart’s acceleration. 2. After your hand is no longer touching the cart and it is moving toward the bumper, sketch the position of the bubble. What can you say about the cart’s acceleration during this time, is it zero or nonzero? Draw a Free Body Diagram of the cart at this time and if applicable, draw an arrow that points in the direction of the cart’s acceleration. 3. What happens to the position of the bubble the moment the cart hits the bumper? Sketch the position of the bubble. What can you say about the cart’s acceleration during this time, is it zero or nonzero? Draw a Free Body Diagram of the cart at this time and if applicable, draw an arrow that points in the direction of the cart’s acceleration. 4. Using Newton’s first law, try to explain what is happening to both the bubble and the fluid during the different periods of motion. Were your predictions correct? 2.2.1 Newton’S First Law / Analyzing Accelerations Due to Gravity Take your track and place it on the metal bar so that it is inclined at a small angle of about 15 degrees. Make sure that the black bumpers underneath the track are behind the metal bar, to ensure that the track will not slide off during the next part of the laboratory. While the cart is resting on the inclined track against the bumper, adjust your Bubble level so that the bubble is positioned in the center between the two lines while the cart is at rest. Meaning, the level should be parallel to the table, even though the cart is now on an incline. Assume that all surfaces are perfectly smooth, which means the cart does not slow down due to friction. Figure 2.4: Cart on a Sloped Track Like before, we are going to try and make some predictions. For each of the motions described below, predict where the bubble will be in the level and sketch the location of the bubble within each box. For each case, try and briefly explain your prediction. It may also be helpful to think about what happens to the fluid that is in the level during these time periods. 109 Acceleration is nonzero Do fffhand a Acceleration o f Acceleration is nonzero tuffs Thefluid wants to remain at constantveloden because of Newton's 1st Law so it moves to the opposite diveltion utaneteration Meanwhile the bubble is a lack of fluid so it moves to the direction of acceleration Our Predilian were louvet

2.2. Newton’s First Law / Analyzing Simple Accelerations 2.2.2 Circular Motion Using the same principles as earlier, we will now make some predictions and observations regarding circular motion. In the front of the room, there is a rotating chair with a bubble level attached to it. Figure 2.5: Chair Like before, we are going to try and make some predictions. For each of the motions described below, predict where the bubble will be in the level and sketch the location of the bubble within each box and indicate which direction the center of the circle is relative to the level by drawing an arrow. For each case, try and briefly explain your prediction. It may also be helpful to think about what happens to the fluid that is in the level during these time periods. Case 1: The chair is being slowly spun clockwise with a constant speed. Case 2: The chair is released and continues rotating clockwise. Case 3: The chair is being slowly spun counter clockwise with a constant speed. Explanation: Explanation: Explanation: Now we will try it out. Go to the front of the room and make sure that the bubble is in the center of the level (i.e. the level is level) while the chair is at rest. Take your hand and gently spin the chair in the clockwise direction. Stop it and then slowly spin it again in the counter clockwise direction. 1. Using Newton’s first law, try to explain what is happening to both the bubble and the fluid during the different periods of motion. Were your predictions correct? 2. Briefly describe what happens to the speed and velocity of the bubble level during its circular motion. In particular, are they constant or changing? How does this influence the position of the bubble? 111 NV allelebation bubble the bubble mum n www niariiiyiiEtfEEiit t.info ueEEiaEEem out in on in on in The fluid wantstoremain at constantbelouth because of Newton's 1st law suit moves to the opposite divationof allelevation Meanwhile thebubbtelacktwi.de soltmoveltothedivectimotaxebevoru.mn Velocity can be changing but actelevation isalways constant towards tnereheevotthett.ru

2. F ORCES A ND A CCELERATIONS 2.3 Analyzing Forces And Accelerations For the remainder of this section, take off the Bubble Level and putty and refer to the figure below. Move the bumper to the opposite edge of the track. The bumper should be next to the pulley, near the edge of the table, and positioned at approximately 100 cm. Remove the track from the raised bar, and place it flat against the table, and then place your cart on the track. Place the 500g mass bar on top of the cart, and put on an additional 30 grams of mass onto the cart using the small circular masses. Attach one loop on your string to the plastic screw on the end of the cart. Hook the weighted hook onto the other end of the string, and place the string over the pulley. Your cart may begin to move, if this is the case just place the hook on the table for now, and keep the system at rest. Figure 2.6: Cart and Pulley System 1. Draw a Free Body Diagram for both the cart on the track, and the hook hanging from the pulley. Before we physically do anything with the cart and our masses, let’s first think about what will happen. Recall that at the start of the lab, you are given all of the necessary information regarding the mass of the cart, hook etc. You may continue to ignore the effects of friction. 2. Using the Free Body Diagrams you drew in part (1), derive an expression for the acceleration of the hook and the cart in terms of the mass of the hook, the mass of the cart, and the gravitational constant of acceleration g . 3. Using the expression you derived in part (2) calculate the acceleration of the cart and the hook. Assume the mass of the hook is 30 grams, the mass of the cart is 1.05 kg, and that g = 9.8 m / s 2 4. Using the expression you derived in part (2) calculate the acceleration. This time, assume the mass of the hook is 60 grams, the mass of the cart is 1.02 kg, and that g = 9 . 8 m / s 2 . How does this acceleration compare to the value you just calculated above, is it greater than, less than or equal to the acceleration you calculated in part (3)? Explain your reasoning. 112 µ tart Iff hook fig tree Md Mug in avian a Frasier a my v 27 mar aggregate EYE.tn atiiaren n nd man of system is uncharted

2. F ORCES A ND A CCELERATIONS 10. How do your observed rates of acceleration compare to the theoretical values of acceleration you calculated in parts (3) and (4)? Are they higher than, lower than, or about the same as your predictions? 11. What things might have affected the acceleration of the cart in real life that we did not account for in our simplified calculations? 2.3.1 Statics And Motion On An Inclined Ramp Remove the 500g mass bar from the top of your cart. Remove the extra circular masses form your hook. Take your track and place it on the metal bar so that it is inclined again. Make sure that the black bumpers on the bottom of the track are behind the metal bar, to ensure that the track will not slide off during the next part the laboratory. Again take the string and attach it to the cart; take the other end of the string with the hook attached and place it over the pulley. Figure 2.7: Cart and Pulley on a Sloped Track 1. Draw a Free Body Diagram for the Cart and the Hook separately for this positioning. 2. Theoretically, it is possible to place the cart on the middle of the ramp and have the system be at equilibrium (at rest). How could this be done? 3. Calculate what angle you would need to incline the ramp at, to have the system of the cart (mass = 520 grams) and the hook with 100 grams of added mass (105 gram total mass) to remain at rest. What angle would be needed? 114

2.4. Friction Is Fun!! 4. Based on your above calculations, try to put the system into balance. Was the angle you calculated in part (3) the correct angle needed to balance the system? Explain any differences you might have observed. 2.4 Friction Is Fun!! Bonus Questions : When the track is flat against the table, what type of friction is acting on the cart? Is friction helping or hindering the motion of the cart? What about when the track in on an incline? Briefly explain: 115