Transcript Lec13-105A-12-10Fall-Astroblaster.pptx

Physics 105A
Analytical Mechanics
1-D Collisions
28 June 2016
Manuel Calderón de la Barca Sánchez
m
v
M
 Final lab velocities:
m-M
vm = v
m+ M
2m
vM = v
m+ M
 Interesting limits:
m=M
M>>m
M<<m
28 June 2016
MCBS
Basketball and Tennis Ball

A basketball with mass m1 is held below a
tennis ball with smaller mass m2 . The
bottom of the basketball is at height h above
the ground, and the bottom of the tennis ball
is at height h+d above the ground. The balls
are dropped from rest. To what height does
the tennis ball bounce?
Assume m1>>m2.
Assume balls bounce elastically.
Assume balls bounce instantaneously.
Assume tennis ball is just slightly above
basketball.
28 June 2016
MCBS
d
h
Many bouncing balls
 Now consider n balls, B1, B2, … Bn, having
masses m1, m2, … mn (with m1>>m2>> …
>> mn), standing in a vertical stack. The
bottom of B1 is a height h above the
ground. The bottom of Bn is a height h+l
above the ground. In terms of n, to what
height does the top ball bounce?
Make similar assumptions as before.
Assume h=1 m and l is negligible. What is the
minimum n to reach a height of 1 km? To
reach escape velocity?
28 June 2016
MCBS
“Astroblaster”