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

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

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

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

5. 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

6. 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

7. Elastic Collision – Measuring vinitial
Glider
Force Sensor

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

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

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

11. Inelastic Collision – Measuring vinitial
Force Sensor
Glider

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

13. Inelastic Collision : vfinal=0
Force Sensor
Glider

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

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

16. 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)