derive this equation a=(1/(mc+mh))wh where mc; mass of the cart, mh: mass hanging, wh: weight hanging. the total mass (experimental): 965.2g

the theoretical total mass: 912g find the acceleration of the system

Verifying Newton's 2nd Law hi slost PreY PIUG NYA -F2023 201 jay bris slit box me nago nobelloo stab dilw gainniged noted OBJECTIVE: sieb way broan of stoudwe . Verify Newton's Second Law.or Istal or terh Isunseen at 1, ston . Prepare data tables for recording experimental results; bavomor ezsm venus . Use a computer to collect and assist with the data analysis, and to produce graphs; . Transfer tables and graphs from an Excel file to a Word file, Theory: A cart on a nearly frictionless track is accelerated by a hanging mass. The two are tied to each other by a thin string passing over a light and nearly frictionless pulley. See figure 1 below. ami ay inCarter meStopper ULI Track interface smart Lalded pulley Fro only no goor and matevasili mail esecam Tom I Mass It ladsi al Tortmounts holder Figure 1. Apparatus setup for verification of Newton's 2ad Law. The motion of the cart will be measured and recorded by a computer and a "smart pulley". The smart pulley has holes that alternately block and unblock a beam of light as the pulley turns. The computer times the interruptions of the beam, and uses the circumference of the pulley to calculate the speed of the cart. Newton's 2nd Law "The mass of the body times the acceleration of the body equals the net force vector" thus: EF = ma It can be shown that the acceleration of our system depends on the hanging weight Wh (Wh = mng, where mm is the hanging mass), and on the sum of the masses of the (cart + its load) mc and the hanging mass mh , according to the equation a = (1/(mc + mm))wh In order to verify Newton's 2nd Law, you will vary the hanging weight Wh and measure the acceleration a while keeping the total mass mc + mi constant. This will be done by transferring mass from the cart to the hanging mass holder.Procedure and computer analysis: Before beginning with data collection, open an Excel file and prepare a table in which to record your data. Note: It is essential that the total mass be kept constant at all times. This means that any mass removed from the cart must be added to the hanging mass. Check that the track is level by seeing if the cart rolls when unobstructed (if it rolls towards one end, then adjust the inclination of the track by turning the legs). The procedure for loading the proper software program and data collecting mechanism will be discussed in class by the instructor. Prepare the cart for the first run by placing 350g on the cart and nothing on the 50g holder hanging over the pulley. (Note that the total mass of the system is 350g + 50g + mcart, and it must remain constant throughout the experiment.) Find the acceleration from the velocity vs time graph Record the mass on the cart, the hanging mass, the acceleration and the correlation coefficient in your data table Collect additional data for masses of 300g, 250g, 200g, 150g and 100g on the cart. Remember not to remove the masses from the system, but transfer them from the cart to the hanger. Print your velocity versus time graphs (remember to label the graphs by including the amount of the hanging mass). Print one copy of each graph. Measure the mass of the cart by weighing it on the scale at the front of the classroom. Record this mass. Data, Calculations, Results and questions: 1- Plot a graph of cart acceleration a as a function of hanging weight Wh , and calculate the slope. This slope will allow you to calculate the total mass mc + mh .(Note: slope does not equal mass.) If Newton's 2nd Law is valid, then the total mass calculated in this way should equal the sum of the masses of all parts of the system determined either by weighing or by reading the stamped numbers Calculation : mc + mh - ? 5 12 + 350 + 50 = 9129 a= 0.965 2 2- Compare the total mass of the system found in these two ways by calculating m= 965, 29 the % difference between them. 3- If the total mass obtained is different explain why it is different and suggest experimental procedure that correct or to minimize the difference? 4- State whether the acceleration of the cart varied linearly with the hanging weight, as predicted in equation 1 (if total mass is held constant). 5- Was Newton's 2nd Law verified? How do you know?6109 10 1 942 0 0 6- Suppose that on two different runs with the same masses on cart and hanger, the regression lines for the v(t) graphs have almost the same values for m, but the values for b are quite different. Should one of these runs be rejected? Explain. Lata analysis, and to prod 7- In this experiment you checked whether the acceleration is linearly proportional to the applied force, when the total mass is held constant. But Newton's second law also says that for a given force, the acceleration should be inversely proportional to the total mass (twice the mass will have half the acceleration). How would you modify our procedure to see if this is true? Explain in a sentence or two how you would move or change the masses on cart or hanger for different runs.A " A E E Editing Font Paragraph Styles Cart Acceleration as a Function of Hanging Weight 3.5 y = 0.9652x + 0.0551 2.5 Weight of the hanging mass (N) in 0.5 0.5 1.5 2 2.5 3.5 Acceleration (m/s^2) mc mh ET a wh 862 50 0.45 0.49