Transcript Springs ppt
Springs © 2013 Pearson Education, Inc. Restoring Forces and Hooke’s Law The figure shows how a hanging mass stretches a spring of equilibrium length L0 to a new length L. The mass hangs in static equilibrium, so the upward spring force balances the downward gravity force. © 2013 Pearson Education, Inc. Slide 10-61 Restoring Forces and Hooke’s Law The figure shows measured data for the restoring force of a real spring. s is the displacement from equilibrium. The data fall along the straight line: The proportionality constant k is called the spring constant. The units of k are N/m. © 2013 Pearson Education, Inc. Slide 10-62 © 2013 Pearson Education, Inc. Explore Learning – Gizmo - http://www.explorelearning.com/ Gizmo - Determining the spring constant for a hanging spring Record in your lab notebook Title: Spring Constant Purpose: To determine the value of the spring constant for a hanging spring Procedure Choose a spring – if your birthday is in months: Jan – Mar –> spring 1 Apr – Jun ->spring 2, Jul – Sept -> spring 3, Oct – Dec -> spring 4 Collect data for at least 5 different masses – record in notebook **Make sure the scale is at rest before collecting data use excel to make a graph Create a graph Plot Force vs stretch **watch your units and your axes** Draw a sketch of the graph in your notebook – be sure to use good graphing techniques Determine slope of the graph © 2013 Pearson Education, Inc. Conclusion Questions: 1. What variable can be determined from the slope. 2. Draw a FBD for the hanging mass. How does the restoring force of the spring relate to the weight of the hanging mass 3. Choose another spring. Collect data, draw the force vs stretch graph and find the slope. What does a steeper slope tell you about the spring? © 2013 Pearson Education, Inc. QuickCheck 10.9 The restoring force of three springs is measured as they are stretched. Which spring has the largest spring constant? © 2013 Pearson Education, Inc. Slide 10-64 QuickCheck 10.9 The restoring force of three springs is measured as they are stretched. Which spring has the largest spring constant? Steepest slope. Takes lots of force for a small displacement. © 2013 Pearson Education, Inc. Slide 10-65 Example 10.5 Pull Until It Slips © 2013 Pearson Education, Inc. Slide 10-66 Elastic Potential Energy Springs and rubber bands store potential energy that can be transformed into kinetic energy. The spring force is not constant as an object is pushed or pulled. The motion of the mass is not constant-acceleration motion, and therefore we cannot use our old kinematics equations. One way to analyze motion when spring force is involved is to look at energy before and after some motion. © 2013 Pearson Education, Inc. Slide 10-73 Elastic Potential Energy The figure shows a beforeand-after situation in which a spring launches a ball. Integrating the net force from the spring, as given by Hooke’s Law, shows that: Here K = ½ mv2 is the kinetic energy. We define a new quantity: © 2013 Pearson Education, Inc. Slide 10-74 Elastic Potential Energy An object moving without friction on an ideal spring obeys: Conservation of Energy Ei = Ef where Because s is squared, Us is positive for a spring that is either stretched or compressed. In the figure, Us has a positive value both before and after the motion. © 2013 Pearson Education, Inc. Slide 10-75 © 2013 Pearson Education, Inc. QuickCheck 10.10 A spring-loaded gun shoots a plastic ball with a launch speed of 2.0 m/s. If the spring is compressed twice as far, the ball’s launch speed will be A. B. C. D. E. 1.0 m/s. 2.0 m/s. 2.8 m/s 4.0 m/s. 16.0 m/s. © 2013 Pearson Education, Inc. Slide 10-76 QuickCheck 10.10 A spring-loaded gun shoots a plastic ball with a launch speed of 2.0 m/s. If the spring is compressed twice as far, the ball’s launch speed will be A. B. C. D. E. 1.0 m/s. 2.0 m/s. 2.8 m/s 4.0 m/s. 16.0 m/s. © 2013 Pearson Education, Inc. Conservation of energy: Double x double v Slide 10-77 Example 10.6 A Spring-Launched Plastic Ball © 2013 Pearson Education, Inc. Slide 10-80 Period of a spring Play around with the gizmo Mark the time to complete one oscillation after making changes to k, g, and m Answer the 5 assessment problems at the bottom. I record the results as a classwork grade If the mass is increase, how is the period affected? If the spring constant is increased, how is the period affected? © 2013 Pearson Education, Inc.