PWV 09 Newton 2nd christian

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Name: Christian Gavidia Date: 10/24/2023 Lab Answers LabQuest App 9 Newton’s Second Law (ForceSensor) How does a cart change its motion when you push and pull on it? You might think that the harder you push on a cart, the faster it goes. Is the cart’s velocity related to the force you apply? Or, is the force related to something else? Also, what does the mass of the cart have to do with how the motion changes? We know that it takes a much harder push to get a heavy cart moving than a lighter one. A force sensor and an accelerometer will let you measure the force on a cart simultaneously with the cart’s acceleration. The total mass of the cart is easy to vary by adding masses. Using these tools, you can determine how the net force on the cart, its mass, and its acceleration are related. This relationship is Newton’s second law of motion. OBJECTIVES ⚫ Collect force and acceleration data for a cart as it is moved back and forth. ⚫ Compare force vs. time and acceleration vs. time graphs. ⚫ Analyze a graph of force vs. acceleration. ⚫ Determine the relationship between force, mass, and acceleration. MATERIALS LabQuest LabQuest App Vernier Low-g Accelerometer and Dual-Range Force Sensor or Wireless Dynamics Sensor System (WDSS) Vernier Dynamics Track Vernier Dynamics Cart extra mass Physics with Vernier ©Vernier Software & Technology 9 -1

Experiment 9 PRELIMINARY QUESTIONS Use a tennis ball and a flexible ruler to investigate these questions. 1. Apply a small amount of force to the ball by pushing the flat end of the ruler against the ball (see Figure 2). Maintain a constant bend in the ruler. You may need a lot of clear space, and you may need to move with the ruler. Does the ball move with a constant speed? The newton second law is The ball does not move at a constant speed. It moves at a constant acceleration if we apply a constant force F. 2. Apply a larger force and keep a constant larger bend in the ruler. Does the ball move with a constant speed? No, the ball does not move with a constant speed as question 1 even if it is a larger object. 3. What is the difference between the movement when a small force is applied versus a large force? The difference is in case A the acceleration will be smaller than case B because the force is smaller. Figure 2 Figure 3 PROCEDURE Trial I 1. Set up the equipment for data collection. Using Dual-Range Force Sensor and Accelerometer a. Set the range switch on the Dual-Range Force Sensor to 10 N. b. Attach the force sensor to a Dynamics Cart so you can apply a horizontal force to the hook, directed along the sensitive axis of the sensor (see Figure 3). c. Attach the Low-g Accelerometer so the arrow is horizontal and parallel to the direction that the cart will roll. Orient the arrow so that if you pull on the force sensor the cart will move in the direction of the arrow.

d. Find the mass of the cart with the force sensor and accelerometer attached. Record the mass in the data table. e. Connect the force sensor and the accelerometer to LabQuest. Choose New from the File menu. Physics with Vernier Newton’s Second Law (Force Sensor) Using WDSS a. Attach the WDSS to the cart and find the mass of the cart with the WDSS attached. Record the mass in the data table. b. Turn on the WDSS. Note the name on the label of the device. c. Choose New from the File menu. Choose WDSS Setup from the Sensors menu. d. Tap Scan to look for WDSS devices. e. Select your WDSS and select OK. f. Select Accel-X and Force to enable the sensors you need for this experiment. Select OK. 2. To zero the sensors, place the cart on the Dynamics Track on a level surface. Verify the cart is not moving and choose Zero ► All Sensors from the Sensors menu. The readings for both sensors should be close to zero. 3. You are now ready to collect force and acceleration data. Grasp the force sensor or WDSS hook. Start data collection and roll the cart back and forth along the track covering a distance of about 10 cm. Vary the motion so that both small and large forces are applied. Your hand must touch only the hook and not the sensors or cart. Only apply force along the track so that no frictional forces are introduced. 4. Acceleration and force data are displayed on separate graphs. Sketch the graphs in your notes. How are the graphs similar? How are they different? 5. Examine the shape of the force vs. time and acceleration vs. time graphs. When the force is maximum, is the acceleration maximum or minimum? 6. One way to see how similar the acceleration and force data are is to make a new plot of force vs. acceleration, with no time axis. a. Choose Show Graph ► Graph 1 from the Graph menu to view a single graph. b. Choose Graph Options from the Graph menu and select the checked boxes for Point Protectors and Connect Points. This removes the point protectors and the line connecting the data points on the subsequent graph. Select OK. c. Change the x-axis to Acceleration and the y-axis to Force. d. Sketch this graph in your notes. 7. Fit a line to the graph of force vs. acceleration. a. Choose Curve Fit from the Analyze menu. b. Select Linear as the Fit Equation. Record the equation for the regression line.

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c. Select OK. d. Print or sketch your graph. Trial II 8. Add extra mass to the cart. If you are using a green metal cart, remove the accelerometer, attach the 0.50 kg mass to the cart, and then re-attach the accelerometer (see Figure 4). If you are using a plastic cart, add 1–4 hexagonal bar masses to the cart (see Figure 5). Record the total mass of the cart, sensors, and additional mass in the data table. 9. Repeat Steps 3–7 for the cart with the additional mass. Physics with Vernier 9 -3 Experiment 9 DATA TABLE Trial I Mass of cart with sensors (kg) 0.2798 kg Regression line for force vs. acceleration data y=3.6054x-0.20655 Figure 4 Figure 5

Trial II Mass of cart with sensors and additional mass (kg) 0.7753 kg Regression line for force vs. acceleration data Y=1.2651x-0.14254 ANALYSIS 1. Are the net force on an object and the acceleration of the object directly proportional? Explain, using experimental data to support your answer.

Yes, the net force on an object and the acceleration are directly proportional. This is because the plot of force vs acceleration is a straight line. Which shows the linear relation between them. 2. What are the units of the slope of the force vs. acceleration graph? Simplify the units of the slope to fundamental units (m, kg, s). Any changes in the slope will represent (indicate) a change in mass by collision, loss of mass etc. Unit of force F= Newton = kg m/ s^2 Unit of acceleration, a= m/s^2 Slope = dy/dx = dF/ da = (Newton *(s^2))/ m In S.I. units, slope= dF/da = (kg m/(s^2))/(m/s^2) = kg =unit of mass 3. For each trial, compare the slope of the regression line to the mass being accelerated. What does the slope represent? Here the slope of the line represents the mass of cart. 4. Write a general equation that relates all three variables: force, mass, and acceleration. The general equation which relates force, mass and acceleration is Force =mass × acceleration EXTENSION Use this apparatus to measure mass. Place an unknown mass on the cart. Measure the acceleration and force and determine the mass of the unknown. Compare your answer with the actual mass of the cart, as measured using a balance. 9 -4 Physics with Vernier

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