PHY 113_Lab_Newtons Laws (1)

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Arizona State University, Tempe *

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101

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Mechanical Engineering

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Dec 6, 2023

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1 NEWTON’S LAWS OF MOTION OBJECTIVE In this lab you will use a simple Atwood’s machine to validate Newton’s Laws of Motion. EQUIPMENT dynamics track, cart, motion sensor, index card reflector, lab stand, balance, hanger and weights, Pasco 850 interface, string, level Figure 1: Picture of the equipment

2 INTRODUCTION AND THEORY Newton’s Laws are an essential part of Dynamics —the area of physics that studies the motion of bodies due to the forces on them. Whenever two bodies come into contact there is a force between them called a contact force. A force is a vector quantity, and as such it can be presented as an arrow, having both a direction and magnitude. Typically, the point of the arrow shows the direction in which the force is being applied, and the length of the arrow shows the magnitude of the force. The two main types of forces are contact and field forces. As mentioned before, contact forces require two bodies to be touching each other. Examples of contact forces are: friction, normal, and tension forces. Examples of field forces are: gravity, magnetic, electric forces. The field forces are also called body forces, since they act all throughout the body of an object. To predict the motion of an object, the forces acting on that object are added together. The resulting sum is called the net force . Newton’s First Law states that an object will remain at rest or will remain at a constant velocity if the external net force is zero. In other words, if the vector sum of all the external forces applied to an object is zero. If the forces do not add to zero (not balanced) the object will move with constant acceleration, given by Newton’s Second Law. Σ࠵? = ࠵?࠵? 1 Keep in mind the sum of forces in Eq1 are the external forces acting on the object. If Σ࠵? = 0 then the forces are balanced and the object is at rest or constant velocity as stated by Newton’s First Law with zero acceleration. Newton’s laws only hold if the coordinate system is an inertial frame of reference. This means the coordinate system cannot be accelerating or rotating. There are ways to adapt Newton’s Laws to work in accelerating and rotating reference frames but we will not need that in this lab. In situations where the mass is constant, Newton’s second law is a linear equation in the form of ࠵? = ࠵?࠵? + ࠵? 2

3 If we were to plot acceleration vs net force (i.e. ࠵? = - . Σ࠵? ), then by comparing with Eq2 we see the slope of the line should be ࠵?࠵?࠵?࠵?࠵? = 1 ࠵? 3 The uncertainty in the experimental value of the mass can be found by applying the rules of error propagation. Δ࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵? = Δ࠵? ࠵? Δ࠵? = Δ࠵?࠵?࠵?࠵?࠵? ࠵? 7 4 Newton’s Third Law establishes the connection between the action-reaction pair of forces. If two objects contact each other, then the contact force on one will be equal in magnitude and opposite in direction to the contact force on the other. It is very common to think the action and reaction pairs must cancel each other. However, they cannot as the action force is on the first object while the reaction force acts on the second object. And each object has its own individual Newton’s Second Law equation Eq2. In this lab, you will validate the first and second laws using a motion sensor and a cart moving along a horizontal aluminum track.

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4 PROCEDURE Part1: Newton’s First Law: An object in motion stays in motion First open up your premade Capstone file from the location: / Desktop/labs/PHY 113/Capstone/Newton’s First and Second Law.cap 1. Measure the mass of the cart ( ࠵? ) and the mass of the hanger (࠵?) . 2. Put a cart on the track. Check that the track is leveled with the bubble-level, the cart should not start rolling from rest if the track is level. Pressing the Start button will initiate data recording. It stops automatically after 5 seconds. Make a trial run to check if any adjustments to the motion sensor areneeded. 3. Start the cart as far as possible from the pulley, but not closer than 15 cm to the motion sensor. Press Start. Give a slight push to the cart to make it move. The velocity vs time graphs will appear on the screen. 4. Apply a “Linear Fit” to the part of the data that corresponds to the cart moving at constant velocity . Record the slope. What physics quantity does the slope of this velocity v/s time graph represent? Describe the motion of the cart and explain your data. Part2: Newton’s Second Law: F=ma 1. Arrange four 10.0-g masses on top of the cart so that they are evenly distributed. Hang another 10.0-g mass on the hanger going over the pulley. Again, start the cart as far as possible from the pulley, but not closer than 15 cm to the motion sensor. Press Start and release the cart, do not push it. As before, stop the cart by hand before it bangs into the pulley. 2. Apply a “Linear Fit” to the part of the data that corresponds to constant acceleration motion. Use the slope of the graph to find the cart’s acceleration. Fill in the values of the hanging mass andaccelerationintheCapstone file. 3. Remove a 10.0-g mass from the cart then hang it on the hanger. By doing this, you keep the total system mass (M+m) constant. Distribute the remaining masses on the top of the cart. Again, start the cart as far as possible from the pulley, but not closer than 15 cm to the motion sensor. Be sure the hanger with masses is still hanging over the pulley. Press Start and release the cart. As before, stop the cart by hand before it bangs into the pulley. Apply a “Linear Fit” to find the cart’s acceleration.

5 4. Fill in the new values of the hanging mass and acceleration in the Capstone file. Repeat step 3 until you have no more masses on the cart. For each consecutive run, remove a 10.0-g mass from the cart, then place it on the hanger. No matter how many 10.0-g masses remain on the cart, always try to keep the masses on the cart symmetrically distributed. Record the values of applied force (mg) and the acceleration of the cart for each run in Capstone. 5. Since the friction force is negligible, the magnitude of the gravity force is equal to the magnitude of the net force applied to the system (cart + hanging weight), although their directions are different. After all thedata isentered you will see the graph offorce applied to the cart vs acceleration. Apply a linear fit to the plot. Using the parameters of the regression line (slope and its uncertainty), calculate the experimental mass (m exp ) of the system along with its uncertainty. Eqs 3 and 4. Compare the experimental value of the system’smass(cart+hanger+additionalweights) calculated from the slope of the graph to the one measured with the balance by calculating the percent discrepancy. Is your experimental data in alignment with Newton's Second Law? Part3: Prediction 1. Predict the acceleration of the cart for a given applied force. Remove all the masses from the cart. Select a new value of the applied force that was not used in Experiment 2. Calculate the expected value of acceleration. Hang the masses from the hanger to produce the required force. Record the velocity of the cart's motion. Apply a linear fit to find the acceleration. Does your prediction agree with the experiment? Does your data support the mathematical modelfor Newton’sSecondLaw? Remember to save your graphs and turn them in with your worksheet/report.