Name Date Period Newton s Second Law: Net Force and Acceleration Procedures: Newton s second law describes a relationship between the net force acting on an object and the objects acceleration. In determining this relationship you will be able to define an objects inertial mass. Also the acceleration of the object will be investigated as the inertial mass is varied but the applied net force is held constant. Materials: One of each of the following is needed: Cart Meter stick Pulley with clamp 70 cm string Motion Detector Experiment 1: Investigating net force and acceleration In this experiment you will vary the force applied to the cart and measure the acceleration of the cart. 1) Position the cart about 60 cm from the pulley. Measure 50.0 cm from the edge of the cart toward the pulley (as shown in the diagram below). 60 cm 1) Place the cart on the scale and record its mass in kg:. 2) Place a 10 g mass on the string. About 50 cm 3) Hold the cart at the starting position and as you let it go start the timer for the motion detector to start collecting data. Stop the timers when the cart has traveled about 50.0 cm. Be sure to stop the cart before it hits the pulley. 4) Determine the carts acceleration by finding the slope of the velocity-time graph produced by the motion detector. 5) Calculate the applied force by assuming it is equal to the hanging weight. F = mg, where m is the hanging mass, and g is 9.81 m/s 2. Record the applied force in table 1. 6) Perform three trials for each 5 g mass added and take an average of the acceleration. Record the accelerations in Table 1. 7) Use the three trials to calculate and record the average acceleration of the cart in table 1. 8) Repeat steps 2 through 7. Perform the experiment five times total and remember to add another 5 g mass to the hanger before each of the five runs. 9) Create an Applied Force Versus Acceleration Graph on the graph provided. Label the scale, each axis, and include units. On this graph remember to place the acceleration on the x-axis and the applied force on the y-axis. Use the entire graph, i.e. do not make a tiny graph. Make the graph as big as possible. With a straight edge, draw a best-fit line through your data points.
Analysis: Newton s Second Law Lab Table 1: Acceleration and Net Force Run Number 1 Acceleration trials in (m/s 2 ) Average Acceleration (m/s 2 ) Hanging Mass (kg) Average Applied Force (N) 2 3 4 5 Applied Force Vs Acceleration Graph for Experiment 1
Analyzing the data from Experiment 1 1) Examine your Applied Net Force Vs Acceleration graph. What happens to the acceleration as the applied force increases? Write down your observations. 2) The data points that you graphed should be approximately a straight line. What does this type of graph suggest about the relationship between the acceleration of an object and the net force applied to that object? (linear, inverse, or quadratic relationship) 3) The slope of the graph is a constant and when multiplied by the acceleration, gives the value of the applied net force. Find the slope of the best-fit line on the applied net force verses acceleration graph and record it below. (Remember that slope is found as the rise divided by the run.) N 4) This slope that you found has units of m s 2, which are kg. This constant is a unique value and property of each new body that we accelerate. It is called the inertial mass. Predict what would happen to the slope if we add 0.50 kg to the cart and performed the experiment again. Write your prediction below. Include your reasoning in an explanation following your prediction. (No points will be given if an explanation is omitted.)
5) At the beginning of the activity you found the mass of the cart using a scale. Write this mass in the space provided. Now you will find how your measured value of inertial mass compares to the actual mass of the cart. Next write the inertial mass you calculated from the slope of the Force-Acceleration graph in the space provided. Mass of the Cart found using the scale: kg Inertial mass calculated from the slope of the Force-Acceleration graph: kg Now find the percent difference between the Scale mass value and the calculated inertial mass value by using the equation below. Show all your work. Percent Difference = Mass from Scale Mass from Slope 100 Mass from Scale 6) Often when we perform experiments we find that values we measure are not exactly the same as the actual excepted value. What might be some factors that make a difference between the actual and measured values of the inertial mass? What can be done to minimize these factors?
Force and Acceleration Use the following situation to answer questions (7-10) A student is placed in a small hoover craft made by a groups of physics students one day after school. The students tie a rope to the hoover craft and pull on the rope, horizontally, with a Newton scale. Other students in the group determine the acceleration of the hoover craft as different forces are applied to the rope. They produce a data table of their results. The data table is included below. (Neglect friction for this problem.) Trial Number Average Force (N) Acceleration (m/s 2 ) 1 100 1.08 2 200 2.15 3 300 3.26 4 400 4.30 5 500 5.38 7) Using the data table make a Force-Acceleration Graph on the grid below. Label both the scale and the axes (Include the proper units.) 8) What quantity does the slope of the graph represent? 9) If the experiment was done again and the slope of the Force-Acceleration graph was greater, describe what must have changed in the experiment. 10) Draw a best-fit-line through the data on the graph and find the slope of the graph (Include the proper units on the slope value.)
Force Problems 11) A toy car is placed, at rest, at the top of a small wooden inclined plane and released. After the car reaches the bottom of the inclined plane it travels across a table slowing to a stop. The acceleration of the car, as it slows to a stop, is determined to be 0.2 m/s 2. The mass of the car is 18 grams. a) Use the rectangle below to make a freebody diagram of the car as it is moving across the table slowing down. b) Write a net force equation for the x- and y- directions. Decide if Newton s first or second law applies and set each equation equal to zero or ma. F Net,x= F Net,y= c) Find the magnitude of the friction force acting on the car as it travels across the table, slowing down. 12) A wooden block is attached to a spring and pulled horizontally across a table top. The friction force acting on the block is 0.245 N and the spring force is 0.715 N. The block is measured to be accelerating across the table at 3.76 m/s 2. a) Use the rectangle below to make a freebody diagram of the block as it is moving across the table top. b) Write a net force equation for the x- and y- directions. Decide if Newton s first or second law applies and set each equation equal to zero or ma. F Net,x= F Net,y= c) Find the mass of the wooden block and express your answer in grams.