Lab/Demo 4 Circular Motion and Energy PHYS 1800

Transcription

1 Lab/Demo 4 Circular Motion and Energy PHYS 1800 Objectives: Demonstrate the dependence of centripetal force on mass, velocity and radius. Learn to use these dependencies to predict circular motion Demonstrate the connection between applied force and work. Understand the concepts of gravitational potential energy and kinetic energy. Develop some intuition for the principle of conservation of energy. Use Conservation of energy to predict the motion of objects. Demonstrate and predict the mechanical advantage of simple machines. Describing Forces and Newton s Laws Force the quantity required to change the motion of an object Tension the force exerted on an object through a string Centripetal Force A force (or combination of forces) that results from the change in direction of an objects velocity. Work Force applied to an object times the distance the force acts over. 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).. Mechanical Advantage The ratio of output force to input force for a simple machine Tangential Velocity Demo (and the Spinning Cat Movie) Question: Which way will the ball go? Horizontal Circular Motion Demo For this toy er, huh scientific apparatus, the centripetal force is balanced by the tension in the string, which is then balanced by the weight of the hanging mass. T=mg=mv 2 /r Questions: What happens when the toy is not spinning? What happens if we increase the velocity? What happens if we increase the hanging mass (that is increase the weight)? What happens if we increase the spinning mass? What happens if we increase the radius? Demonstration: Bucket Water Demo. PHYS 1800 Lab-Demo 4 Circular Motion and Energy 1 2/5/2009

2 The Lever as a Simple Machine Consider a mass hung off one end of a meter stick. Let s measure the force required on the other end of the meter stick to move this mass up a distance of 5 cm. Also measure the distance we move the other end of the meter stick to move the mass 5 cm. Fill in the table below for the cases Work for Mass Mass Distance (kg) Mass is Moved (m) Work Done on Mass or W=F*D=mg*D, Work Done by Hand Measured Distance Force Hand Exerted by Traveled Hand (N) (m) Work Done By Hand Ratio of Works, W mass /W hand Comment on the mechanical advantage of the lever: The Pulley as a Simple Machine Comment on the mechanical advantage of the lever: Consider a mass hung off a single pulley. Measure the force from your hand and the distance the force acts to raise the 5 kg mass 10 cm. Fill in the table below for the cases. Double the mass. Now use the triple pulley and repeat for the 5 kg and 10 kg masses. Work for Mass Mass Distance (kg) Mass is Moved (m) Work Done on Mass or W=F*D=mg*D, Work Done by Hand Measured Distance Force Hand Exerted by Traveled Hand (N) (m) Work Done By Hand Ratio of Works, W mass /W hand Comment on the mechanical advantage of thepulleys: PHYS 1800 Lab-Demo 4 Circular Motion and Energy 2 2/5/2009

3 On the Right Track with Conservation of Energy Consider the ball moving on U-shaped track. How high will the ball go up the track on the other side of the dip? Is this height dependant on the tilt angle of the track? Now consider a ball moving on the loop-the-loop track. How high do you need to release the ball on the track to get the ball to navigate the loop successfully? Explain the result. PHYS 1800 Lab-Demo 4 Circular Motion and Energy 3 2/5/2009

4 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 th pendulum depend on mass? String length? Angle? PHYS 1800 Lab-Demo 4 Circular Motion and Energy 4 2/5/2009

5 Consider the motion of a mass oscillating on a spring. Plot the vertical position as a function of time. Use you knowledge of veilocity 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 PHYS 1800 Lab-Demo 4 Circular Motion and Energy 5 2/5/2009