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Force Versus Distance Graph 6/3/14 Objectives Force versus • Investigate examples of kinetic and potential energy and their transformations. distance graph • Calculate work from the area under the force vs. distance graph. • Relate the net work done on an object to its change in kinetic energy. • Demonstrate the use of course apparatus and equipment, including slotted or hooked masses, spring scales, meter sticks, graph paper, graphing technology, and data acquisition probes. Assessment Assessment An elastic band is stretched 40 cm An elastic band is stretched 40 cm and used to accelerate a cart. and used to accelerate a cart. 1. How much work is done on 2. BEFORE the elastic band does the cart when the band is work on the system, what type released? of energy does the system have, and how much? 3. AFTER the elastic band does work on the system, what type of energy does the system have, and how much? Physics terms Equations • force Work done by a • work constant force: • force vs. distance graph Area of a rectangle: Area of a triangle: 1 6/3/14 Reviewing the concept Reviewing the concept A constant force of 4 N acts on an object in the direction of its motion. If the object moves 2 meters, how much work is done? The work done by a force equals the force times the distance moved in the direction of the force. Reviewing the concept Reading the graph A constant force of 4 N acts on an A graph of force vs. distance for object in the direction of its motion. this event is shown. If the object moves 2 meters, how much work is done? A constant force of 4 N acts on an object in the direction of its motion. The object moves 2 meters. Area under the graph Area under the graph The work done equals the area The work done equals the area of the shaded rectangle. under the force vs. distance graph. • If the force is constant, this area is a rectangle. • But what if the force is not constant? 2 6/3/14 Area under the graph Area under the graph The force shown here is NOT The work done equals the constant. triangular shaded area. How do we find the work done in this example? Investigation Investigation Part 1: Elastic force In Investigation 9A on the Gather your materials. Calibrate the spring scale if needed. force vs. distance graph you will explore the relationship 1. Stretch the elastic band to different between work and energy. distances and measure the force with a spring scale. Tabulate your results. The investigation is found on page 262. Investigation Investigation Part 1: Elastic force Part 1: Elastic force 2. Using your computer, 3. For each displacement, click on the graphing tool in release the ErgoBot and the electronic resources to capture its motion data on conduct the investigation. the computer. Plot force versus the Record the maximum speed displacement of the band. and calculate the kinetic Calculate the elastic potential energy. Add these values to energy at each displacement. your table. 3 6/3/14 Investigation Investigation Questions for Part 1 Part 2: Gravitational force a. How does the work done by the elastic band compare Gather your materials. with the Ek of the ErgoBot? Why? Select a hanging mass that allows for a brisk but b. What are the independent, controlled acceleration. dependent, and controlled variables? Investigation Investigation Part 2: Gravitational force Part 2: Gravitational force 1. Release the suspended 3. Calculate the net force at mass and capture the each distance by applying motion data on the Newton’s second law: computer. Fnet = ma. 2. For at least 5 points on the 4. Plot a graph of force vs. motion graph, determine distance for the ErgoBot. the distance traveled and the acceleration. Investigation Assessment Questions for Part 2 An elastic band is stretched 40 cm and used to accelerate a cart. a. Use the motion graphs to determine vmax at the end of the accelerated motion. What was the maximum Ek? 1. How much work is done on the cart when the band is b. Calculate the total work done on the ErgoBot from the area released? under the graph of force vs. distance. c. How does the total work done on the ErgoBot compare with its maximum kinetic energy? 4 6/3/14 Assessment Assessment An elastic band is stretched 40 cm An elastic band is stretched 40 cm and used to accelerate a cart. and used to accelerate a cart. 1. How much work is done on 2. BEFORE the elastic band does the cart when the band is work on the system, what type of released? energy does the system have, and how much? 3. AFTER the elastic band does work on the system, what type of energy does the system have, and how much? Assessment Assessment An elastic band is stretched 40 cm An elastic band is stretched 40 cm and used to accelerate a cart. and used to accelerate a cart. 2. BEFORE the elastic band does 2. BEFORE the elastic band does work on the system, what type of work on the system, what type of energy does the system have, and energy does the system have, and how much? how much? elastic potential energy = 4 J elastic potential energy = 4 J 3. AFTER the elastic band does work 3. AFTER the elastic band does work on the system, what type of energy on the system, what type of energy does the system have, and how does the system have, and how much? much? kinetic energy = 4 J 5 .
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