Purpose Use numerical integration to determine whether a physical system involved in a collision obeys Newton’s Second Law.

Newton’s Second Law ,where Net force acting on object

Newton’s Second Law, in case you didn’t recognize it , if m = constant (dm/dt=0)

Impulse “Impulse” Change in momentum Impulse = Change in Momentum

The Basic Idea of this Lab Measure momentum change using the photogate (vinitial before collision, and vfinal after collision) Numerically integrate the measurements from the force sensor during the collision. Compare

Setup for Elastic Collision flat bumper photogate spring A bit of clay as a counter-weight bumper with needle eraser Force Sensor Glider Air Track

Elastic Collision – Measuring vinitial Glider Force Sensor

Elastic Collision – Measuring the force during the collision Glider Force Sensor

Elastic Collision – Measuring vfinal (going through the photogate in the other direction) Force Sensor Glider

Setup for Inelastic Collision photogate Modeling clay on hook (don’t use spring) Modeling clay Force Sensor Glider Air Track

Inelastic Collision – Measuring vinitial Force Sensor Glider

Inelastic Collision – Measuring the force during the collision Force Sensor Glider

Inelastic Collision : vfinal=0 Force Sensor Glider

The force-time diagram during the collision After collision: Force = 0 (if tared properly) Before collision: Force = 0 (if tared properly)

The force-time diagram during the collision Discrete measurements in certain time intervals get recorded also in a table in Capstone

Numerical Integration using the Table Data time (in s) Force (in N) 0.00 0.01 0.02 0.03 … 0.12 0.13 0.00 0.01 0.02 … 0.03 before collision (f=0) Export these data to Excel. Integrate in Excel using the trapezoidal rule (see homework). after collision (f=0)