Acceleration and Force: I

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1 Lab Section (circle): Day: Monday Tuesday Time: 8:00 9:30 1:10 2:40 Acceleration and Force: I Name Partners Pre-Lab You are required to finish this section before coming to the lab, which will be checked by one of the lab instructors when the lab begins. 1) Read your textbook and class notes on Newton s second law of motion. Write down the formula that states Newton s second law. 2) Read your textbook and class notes on Newton s third law of motion. Take notes in the space provided. 3) Read your textbook and class notes on spring force. Write down an expression that describes the spring force. 1

2 I. Second Law Force Diagram. A. Stationary Block 1) Two people are attempting to move a large block. The block, however, does not move. Pat is pushing on the block and Homer is pulling on a rope attached to the block. Pat Homer 2) The large dot below represents the block. Draw vectors with their tails on the dot to show all the forces exerted on the block. Label each vector and write a brief description of that force next to the vector. The diagram you have drawn is a second law force diagram, also called a free-body diagram. (In the remainder of the lab, we will use both terms.) Often a free-body diagram involves a simplified sketch of the object rather than a dot. Regardless of which form is used, a proper free-body diagram (or second law force diagram of the object) should not have anything on it except a representation of the object and the (labeled) forces exerted on that object. A free-body diagram never includes 1) forces exerted by the object of interest on other objects or 2) sketches of other objects that exert forces on the object of interest. 3) Consider the block in the diagram above. a) Which of the forces exerted on the block arise from direct contact between two objects? b) Which of the forces exerted on the block do not arise from direct contact between two objects? 2

3 c) Are there any third law force pairs among the forces in the free-body diagram (do not consider forces other than those explicitly seen in the diagram)? If so, label them; if not, state why not. 4 a) Redraw the free-body diagram, resolving each of the forces into horizontal and vertical components. b) Draw a tip-to-tail diagram summing the horizontal components of the forces. Remember that tip-to-tail diagrams represent how to add vectors by placing the tail of each successive vector at the tip of the previous vector. Label each component. c) Draw a tip to tail diagram summing the vertical components of the forces. Label each component. Check with an instructor before you continue. 3

4 B. Orange on a Table In the following picture there is an orange resting on a table. The table rests on the floor. 1) The dot below represents the orange. Draw vectors with their tails on the dot to show all the forces exerted on the orange. Label each vector and write a brief description of that force next to the vector. 2) The dot below represents the table. Draw vectors with their tails on the dot to show all the forces exerted on the table. Label each vector and write a brief description of that force next to the vector. 3) Consider the orange in the diagram above. a) Which of the forces exerted on the orange arise from direct contact between two objects? 4

5 b) Which of the forces exerted on the orange do not arise from direct contact between two objects? 4) Consider the table in the diagram above. a) Which of the forces exerted on the table arise from direct contact between two objects? b) Which of the forces exerted on the table do not arise from direct contact between two objects? 5) Considering the free-body diagrams of both the orange and table together, are any third law force pairs present? If so, label them; if not, state why not. 6 a) Draw a tip-to-tail diagram summing the horizontal components of the forces on the orange and the table. (Draw them separately in the space provided and label each component.) b) Draw a tip to tail diagram summing the vertical components of the forces on the orange and the table. (Draw them separately in the space provided and label each component.) Check with an instructor before you continue. 5

6 III. Hooke s Law At your table you have a spring, a measuring disk, a ring stand, and a mass hanger. You and your lab partners are going to hang a mass from the spring and measure the change in length of the spring. This process will be repeated for several different mass quantities, and the results analyzed. Begin by hanging one end of the spring from the hook on the ring stand and attaching the measuring disk and mass hanger to the other end of the spring. With the spring freely hanging, align the zero of the scale to the measuring disk. Make sure each member of your group agrees with the initial position. 1 a) Draw a diagram of the apparatus you have just assembled. b) Draw a free body diagram of the spring while it has the mass hanger attached (again, represent the spring as a point). Make sure to label and describe all of the forces on the diagram. c) Draw a free body diagram of the mass hanger. Again make sure to label and describe all forces on the diagram. d) Considering both free-body diagrams together, are any third law force pairs present? If so, label them; if not, state why not. 6

7 2) To begin taking measurements, add mass, 5 grams at a time; measure the length of the spring each time. Each member of your group should take an independent reading of the change in length of the spring for each mass that is added. An independent reading is done without comparing results of measured values until each group member has recorded his/her own measurement independently do not agree on readings as you measure. Record your data, as well as your lab partners data in a table below. 3 a) List at least three sources that could reasonably lead to uncertainty in your length measurements and describe specifically how each source limits your ability to obtain the perfect measurement. b) Based on your answer to (a), determine and write an uncertainty for your measurements in ± form. You will need information from your lab partner s analysis to complete the write-up so keep in contact this week! Do not wait until the last minute to share results with your lab partner(s) or you will not have enough time to complete the homework. We suggest that before you leave lab today you set a deadline among your group by which time you will have provided all shared information (see question 7 in the homework section) needed to complete the lab. Check with an instructor before you leave. 7

8 Homework Problems 1) A box slides down a ramp at constant speed as shown in the diagram below. The ramp itself is firmly attached to the ground so that it cannot slide along the ground.. a) Is there friction between the box and the ramp? How do you know? If there is friction, what is the direction of the frictional force vector? b) Draw a free-body diagram for each of the following. Clearly label and write a brief description of each force. i) the box: ii) the ramp c) Are there any third law force pairs considering the box and ramp together? If so, state the pairs in the space below. Make sure it is clear which forces are paired. 8

9 2) Plot a Force vs. Length graph for your Hooke s Law experimental data using the grid below. Be sure to label the axes appropriately; check your text if you are unsure how to set up the axes for this graph. Make sure to be careful plotting the data. Draw a best-fit line for your data (do not connect the points with line segments). 3) What type of functional relationship (curve type) do you get from your data? 9

10 4) What does this tell you about the relationship between the force on the spring and the length the spring stretched? 5) Calculate the slope of the best-fit line, making sure not to use any data points. Show your work below and remember that all values have units. When a force is applied to an object, a small amount of deformation can occur, as we saw the length of the spring change by adding mass. Robert Hooke studied this topic and realized that the deformation (stretch of the spring) is proportional to the force applied (mass). This concept is referred to as Hooke s Law and states that F = k L Where F is the force, k is the proportionality constant which depends on the shape and composition of the object and L is the amount of deformation. For our case we will refer to k as the spring constant. 6) What does the slope of your F vs. L graph represent physically? 10

11 7) As a group you should have three values for the slope of the graph, also known as the spring constant. Obtain the rise and run data from your partners graphs and calculate the slopes of their graphs as you did for your own slope in question (5). Do you think they agree within reason? Explain. It is important in lab to account for any error that may occur when taking measurements. There are small differences in how each person reads the equipment and views the measurements. For this reason it is important to take 3 measurements and average the values to get a best result. From these values an uncertainty can also be determined. With worst case uncertainty, this is done by calculating the maximum value the minimum value and dividing the result by 2. To state a final result write it as follows. value final = (value ave ± uncertainty) unit 8) Calculate a final result of the spring constant, k, using your lab partners results as well as your own and write it as shown above. 9) Sketch a Hooke s Law graph showing your original data. Then, on the same graph, sketch the graph for a second spring with a spring constant twice as large as the spring you used. Be sure to label the graph axes appropriately and clearly identify each spring s graphed line. Quantitatively, what is the relationship between the graphs for the two springs? 11

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