Physics Demonstration Lab#6.6: The Impulse-Momentum and Work- Kinetic Energy Theorems For a Single Object on the Air Track

Transcription

1 Physics Demonstration Lab#6.6: The Impulse-Momentum and Work- Kinetic Energy Theorems For a Single Object on the Air Track Name: Date: EQUIPMENT PASCO Scientific Air Track and Accessories PASCO Scientific Force and Motion Sensors PASCO Scientific Science PowerLink Interface Personal Computer with PASCO DataStudio Software PURPOSE The purpose of this activity is to demonstrate how the Impulse-Momentum and Work- Kinetic Energy Theorems can be utilized to analyze interactions between an object and its surroundings. THEORY Impulse-Momentum Theorem: The change in momentum for an object is always equal to the total impulse acting on the object during a given time interval. If the net force is constant, the total impulse is equal to the product of the net force and the time interval over which the net force acts: F t m v v ) net ( f i If the net force varies over the time that the net force acts on the object, then the total impulse may be found most effectively by determining area under the force-time graph. Work-Kinetic Energy Theorem: The change in kinetic energy of an object is equal to the net work done on the object as it moves over a given distance. If the net force is constant, the net work is equal to the product of the net force and the distance over which the net force acts: F net f Vi d m( V 2 If the net force varies over the distance that the net force acts on the object, then the net work is equal to the area under a force-distance. Useful Definitions: Impulse-Momentum Theorem: o Impulse = Area under force-time graph (constant force => Impulse = force*time) o Momentum = mass*velocity o Total Impulse = Change in Momentum o Units: N*sec = kg*m/sec Work-Kinetic Energy Theorem: o Work = Area under force-distance graph (constant force => Work = force*distance) o Kinetic Energy = ½ * mass * speed^2 o Net Work = Change in Kinetic Energy o Units: N*m = kg*m^2/sec^2 = J (Joule) )

2 PROCEDURE Case#1 - Constant Net Force: Consider the apparatus illustrated below: Record the Mass of Air-Track Cart and the Angle of Track. Collect data as the Air-Track Cart travels down the incline using DataStudio and compare those results with the enclosed graphs, which were collected earlier for this case. Motion Sensor Air-Track Cart Case#2 - Variable Net Force - Elastic Rebound: Consider the apparatus illustrated below: Record the Mass of Air-Track Cart / Magnet. Collect data as the Air-Track Cart travels along the air track and rebounds off the magnet attached to the force sensor and compare those results with the enclosed graphs, which were collected earlier for this case. Motion Sensor Air-Track Cart / Magnet Magnet / Force Sensor DATA Case#1 - Constant Net Force: Mass of Air-Track Cart: kg Angle of Track: degrees Graphs for earlier run: Position-Time, Velocity-Time, Acceleration-Time Case#2 - Variable Net Force - Elastic Rebound: Mass of Air-Track Cart: kg Angle of Track: degrees Graphs for earlier run: Position-Time, Velocity-Time, Acceleration-Time, Force- Time, and Force-Position

3 ANALYSIS/CONCLUSIONS: Case#1 - Constant Net Force: Illustrate the forces and the angle of the track to create a Free-Body Diagram for the Air Track Cart Find the Net Force (component of gravity in direction of motion) algebraically Verify that the Force-Time and Force-Distance graphs are consistent with the other data Calculate the change in momentum using mass and velocity data Calculate the impulse using the Impulse-Momentum Theorem Calculate the impulse by calculating the area under the Force-Time Graph Calculate the change in kinetic energy Calculate the work using the Work-Kinetic Energy Theorem Calculate the work by calculating the area under the Force-Distance Graph Complete the following statements by filling in the blank as appropriate: The Impulse-Momentum Theorem supported by this experiment. The Work-Kinetic Energy Theorem supported by this experiment.

4 Case#2 - Variable Net Force - Elastic Rebound: Illustrate relevant forces on the diagrams below to create Free-Body Diagrams for the time-frames indicated: cart moves at constant velocity along the track cart is being pushed backward by the magnet attached to the force sensor Calculate the change in momentum during the entire rebound from the mass and velocity data Estimate the total impulse during the entire rebound by approximating the area under the Force-Time Graph Calculate the change in kinetic energy during the first half of the rebound (as the cart is brought to rest by the magnetic force) Estimate the net work done during the first half of the rebound (as the cart is brought to rest by the magnetic force) by approximating the area under the Force- Distance Graph Complete the following statements by filling in the blank as appropriate: The Impulse-Momentum Theorem supported by this experiment. The Work-Kinetic Energy Theorem supported by this experiment.

5 Case#1 - Constant Net Force:

6 Case#2 - Variable Net Force - Elastic Rebound: