Lab/Demo 5 Periodic Motion and Momentum PHYS 1800 Objectives: Learn to recognize and describe periodic motion. Develop some intuition for the principle of conservation of energy in periodic systems. Use Conservation of energy to understand energy transfer and predict the motion of periodic systems. Develop an intuition for the concepts of impulse and momentum. Use Conservation of momentum to predict the motion of objects. Describing Periodic Motion, Energy and Momentum Period the time for a system in periodic motion to return to its original state. Frequency the number of times per unit time that a system in periodic motion to return to its original state Amplitude The maximum change in a periodic system. Work The energy imparted to an object by a force. Force applied to an object times the distance over which the force is applied. Energy The ability of one object (or system) to do work on another object (or system). Kinetic Energy the energy of an object related to its motion. Potential Energy Stored energy on an object associated with its position. Conservation of Energy The key statement that energy of an object remains unchanged unless a force acts on a body over some distance (that is unless work is done on or by the object).. Impulse The momentum imparted to an object by a force. Force applied to an object times the time over which the force is applied. Momentum The product of an objects mass times its velocity. PHYS 1800 Lab-Demo 5 Energy and Momentum 1 2/13/2009
Demonstration: The Mathematical Equivalence of Circular Motion and Oscillatory Motion Consider the motion of a mass oscillating on a spring. Plot the vertical position as a function of time. Now consider the motion of a mass rotating in a circle. Plot the vertical position as a function of time. On the same graph, plot the horizontal position as a function of time. Now consider the motion of a pendulum mass oscillating on the end of a string. Plot the angle of the mass from the vertical position as a function of time. Angle Indicate the period of the pendulum on your graph. The period is the time to begin repeating motion for periodic motion. Indicate the period on the circular motion and mass-on-a-spring graphs. Does the period of the pendulum depend on mass? String length? Angle? PHYS 1800 Lab-Demo 5 Energy and Momentum 2 2/13/2009
Consider the motion of a pendulum mass oscillating on the end of a string. We have made a bunch of pendulums with the same mass, but different lengths. Measure the time it takes for 20 oscillations of your particular pendulum. Calculate the period of your pendulum. Add the period and the length to the table of values on the board. Now tape your pendulum in the right place on our period number line. Length Period Sketch the results of the groups effort for the pendulum period line. What conclusion can you draw about how the period depends on the length of the pendulum. We have several pendulums of the same length, but different masses. Based on our group calculations does the period depend on mass? We can try several maximum angles for a pendulum with fixed length and mass. Does the period depend on amplitude? PHYS 1800 Lab-Demo 5 Energy and Momentum 3 2/13/2009
Consider the motion of a mass oscillating on a spring. Plot the vertical position as a function of time. Use you knowledge of velocity and acceleration to predict the these for the mass on the spring. Recall that velocity is the slope of the position versus time graph and acceleration is the slope of the velocity versus time graph. Now sketch the graphs of gravitational potential energy and kinetic energy versus time plot these on the same graph. Finally, plot the sum of the gravitational potential energy and kinetic energy as a function of time. Velocity Acclerati Energy 1 PHYS 1800 Lab-Demo 5 Energy and Momentum 4 2/13/2009
Newton s Cradle Demo Describe what you observe about the motion of the balls in the Newton s Cradle Demonstration. Can you explain what is happening? Collision of Carts Consider a set of collusions for two carts on an air track with low friction. Let s consider what happens as we change masses and velocities. Questions: What will happen when a moving cart hits a stationary cart of the same mass? What will happen when a moving cart hits a stationary cart of the twice the mass? What will happen when a moving cart hits a stationary cart of the half the mass? What will happen when two cars with equal mass moving with the same speed, but in opposite directions, collide? What will happen when two cars(one with twice the mass of the other) moving with the same speed, but in opposite directions, collide? Recall that momentum equals mass times velocity. Can you make a generalization about the collisions and momentum? PHYS 1800 Lab-Demo 5 Energy and Momentum 5 2/13/2009