Transcript 02-1-constant-net-force-with

CH02-1 Constant Net Force
x-velocity vs. time graph
Theory
fan cart
displacement
Theory
arithmetic mean velocity
Theory
assuming a constant velocity of vx,avg
gives the same result.
Fnet vs. time graph
Theory
fan cart
Summary of Analytic Method
Theory
Analytic Method in 1-D
Theory
Example
A tennis ball has a mass of 0.057 kg. A
professional tennis player hits the ball hard
enough to give it a speed of 54 m/s (about
121 miles per hour.) The ball moves toward
the left, hits a wall and bounces straight back
to the right with almost the same speed (54
m/s). As indicated in the diagram below, highspeed photography shows that the ball is
crushed about 2 cm at the instant when its
speed is momentarily zero, before
rebounding. How much time elapses between
first hitting the wall and momentarily
stopping? What is the net force on the ball
during the collision?
video
Numerical (computational)
integration
Computation
Assumptions: constant net force, small ∆t
Numerical error
Computation
Assumptions: constant net force, small ∆t
Error can be decreased by
using a smaller time
interval. Also, using the
mean velocity is clearly a
better estimate than using
the final velocity.
Decide at this point to
accept the error, but select a
reasonable time interval to
reduce the error.
Error
Summary of Numerical
Method
Computation
Assumptions: constant net force, small ∆t
At this point, you are
using the EulerCromer Method (semiimplicit Euler Method)
to solve the differential
equations:
with
VPython
Write a simulation that models the motion of a fan cart.
Clearly state your assumptions and your initial
conditions before starting your program.