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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.

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Purpose
Purpose

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


Newton s second law
Newton’s Second Law

,where

Net force

acting on

object



Impulse
Impulse

Change in momentum

“Impulse”

Impulse = Change in Momentum


The basic idea of this lab
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
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 v initial

Glider

Elastic Collision – Measuring vinitial

vinitial

Force Sensor


Elastic collision measuring the force during the collision

Glider

Elastic Collision – Measuring the force during the collision

Force Sensor


Elastic collision measuring v final going through the photogate in the other direction
Elastic Collision – Measuring vfinal(going through the photogate in the other direction)

vfinal

Force Sensor

Glider


Setup for inelastic collision
Setup for Inelastic Collision

photogate

Modeling clay

on hook (don’t

use spring)

Modeling

clay

Force Sensor

Glider

Air Track


Inelastic collision measuring v initial
Inelastic Collision – Measuring vinitial

vinitial

Force Sensor

Glider



Inelastic collision v final 0
Inelastic Collision : v collisionfinal=0

Force Sensor

Glider


The force time diagram during the collision
The force-time diagram during the collision collision

force

collision

time

After collision:

Force = 0 (if tared properly)

Before collision:

Force = 0 (if tared properly)


The force time diagram during the collision1
The force-time diagram during the collision collision

force

collision

time

force

time

Discrete measurements in

certain time intervals

get recorded also

in a table in Capstone


Numerical integration using the table data
Numerical Integration using the Table Data collision

time (in s)

Force (in N)

0.00

0.01

0.02

0.03

0.12

0.13

before collision (f=0)

0.00

0.00

0.01

0.02

0.03

0.01

0.00

Export these data to Excel.

Integrate in Excel using the trapezoidal

rule (see homework).

after collision (f=0)


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