Section 4.9: Investigating Newton's Second Law of Motion

Transcription

1 Section 4.9: Investigating Newton's Second Law of Motion Recall: The first law of motion states that as long as the forces are balanced an object at rest stays at rest an object in motion stays in motion at a constant speed in a straight line. What if an unbalanced force acts on object? What happens? The object will accelerate!! 1

2 Laboratory Simulation In this lesson you will carry out an experiment (Virtual lab) that will lead to a relationship between acceleration and the independent variables of mass and net force. To be successful in this lesson, you need to know the following: A direct proportion occurs when the quotient of two numbers is a constant. Direct proportions are normally written as y = mx where x and y are the two quantities in proportion and m is the common ratio. The graph of y vs. x is a linear one with slope m. An inverse proportion occurs when the product of two numbers is a constant. As one quantity increases then the other decreases, however, the product is always a constant. Inverse proportions are normally written as xy = c or as y = c/x, where x and y are the two quantities in inverse proportion and c is a constant. The graph of an inverse is NOT a line, rather it is a curve known as a hyperbola. 2

3 Part 1 Simulation (Constant m, vary F, Measure a) The animation to the right shows a dynamics cart (mass = kg) on a horizontal table. A tow string is attached to the cart. The string is draped over a pulley which is attached to the end of the table. Notice the five masses on the cart. Each has a mass of kg. These can be removed and placed on the end of the tow string. This will provide an accelerating force to the "cart + mass" system. Notice finally the blue motion sensor on the lab stand at the left of the table. As the cart accelerates across the table the motion sensor collects and graphs velocity vs. time data. This apparatus is designed to investigate the relationship between net force and acceleration. Select any of the 5 menu buttons and press "step" to display one runthrough. Watch for the following: (1) No new mass is introduced to the system. The masses are instead shifted from the cart to the string and vice versa. (2) The v t graph appears as the graph moves. It is possible to determine the acceleration from the slope of this graph. (3) The cart, the on board masses and the falling mass are all accelerating at the same rate. The falling mass (weight) accelerates the whole system. 3

4 Procedure: 1. Run the animation for each of the 5 menu buttons. Do the following for each run (trial). (i) Check to see how many falling masses you have. The force that accelerates the cart is due to force of gravity (weight) on the falling mass. This can be calculated by using the formula F g = mg, where m in this case is the mass of the falling mass. Record this value in the table. (ii) Measure the acceleration from the v t graph (a = slope of the graph) (iii) Record your values of F and a in the table below. 4

5 Newtons s Second Law Simulation Lab (Constant Mass, Vary Force, Measure Acceleration) Mass of Cart (kg): Attached Masses (kg): Total Mass of System (kg): Trial Number Accelerating Force (N) Acceleration (m/s 2 )

6 2. A) Plot a graph of Force vs Acceleration. Even though acceleration was the dependent variable (y) place it on the horizontal axis (x). B) Explain whether the data are linear. If so, construct a line of best fit. C) Find the slope of the line of best fit. You can use your calculator if you wish. D) Compare the slope to the total mass. What do you notice? 3. Describe, in general terms the relation. Go something like this: As the force (increases/decreases/whatever) the acceleration (increases/decreases/whatever) 4. Based on your graph, what is the relationship between force and acceleration? 6

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8 Part 2 Simulation (Constant Force), Vary Mass, Measure a The animation is similar to the one you worked with in part 1. This time, however, you will be using a constant force and will vary the mass so there are two important differences: (1) The masses (each is 0.10 kg) are NOT initially on the cart. Notice, instead, that they are on the table. As you run through the animation the masses will be placed, one at a time, on the cart. This will change the mass of the accelerating system. (2) There is only one falling object, a mass of 0.10 kg provides the acceleration for all of the trials. Select any of the 5 menu buttons to play the animation one time. Notice that the motion sensor collects data to construct a v t graph. Once again this can give the acceleration for any trial. Notice, finally, that there are 5 trials and only 4 masses on the table. One trial will have just the cart and the falling mass. Overall this setup gives 5 trials, each with a different mass. Assume that the mass of the cart is still kg. 8

9 Procedure: 1. Determine the accelerating force provided by the falling mass. 2. Run the animation for each of the 5 menu buttons. Do the following for each: (i) Check to see how many masses you have on the cart. Calculate the total mass (don't forget the falling mass and the mass of the cart). (ii) Measure the acceleration from the v t graph. (iii) Record your values of m and a in the table below. Newtons s Second Law Simulation Lab (ConstantForce, Vary Mass, Measure Acceleration) Mass of Cart (kg): Accelerating Force (N): Trial Number Total Mass of System (kg) Acceleration (m/s 2 )

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11 3. Plot a graph of Acceleration vs Mass. Place acceleration on the vertical axis (y) and mass on the horizontal axis (x). 4. What is the shape of the graph? 5. Describe, in general terms the relation. Go something like this: As the mass (increases/decreases/whatever) the acceleration (increases/decreases/whatever). 6. State whether or not the data suggest that acceleration is inversely proportional to the mass. 7. Plot a graph of Acceleration vs. 1/Mass of the System (reciprocal of the mass). Describe the resulting graph. How does this graph support your conclusion in question 7? 8. In the last two lab simulations, you have investigated the effect of mass and force on the acceleration of the cart. Write an equation to link all three terms. 11

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