1) A billiard ball rolling across a table at 1.25 m/s makes a head-on elastic co
ID: 1533020 • Letter: 1
Question
1) A billiard ball rolling across a table at 1.25 m/s makes a head-on elastic collision with an identical ball. Find the speed of each ball after the collision when each of the following occurs.
The second ball is moving toward the first at a speed of 1.15 m/s.
**1st ball??: ____m/s
2nd ball: 1.25 m/s
2) A 68.0 kg person throws a 0.0500 kg snowball forward with a ground speed of 33.0 m/s. A second person, with a mass of 59.0 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 2.20m/s, and the second person is initially at rest. What are the velocities of the two people after the snowball is exchanged? Disregard the friction between the skates and the ice.
thrower 2.2016 m/s **catcher??_____ m/s
Explanation / Answer
ELASTIC
m1 = m m2 = m
speeds before collision
u1 = 1.25 m/s u2 = -1.15 m/s
speeds after collision
v1 = ? v2 = ?
initial momentum before collision
Pi = m1*u1 + m2*u2
after collision final momentum
Pf = m1*v1 + m2*v2
from momentum conservation
total momentum is conserved
Pf = Pi
m1*u1 + m2*u2 = m1*v1 + m2*v2
m1*(u1-v1) = m2*(v2-u2) .....(1)
from energy conservation
total kinetic energy before collision = total kinetic energy after collision
KEi = 0.5*m1*u1^2 + 0.5*m2*u2^2
KEf = 0.5*m1*v1^2 + 0.5*m2*v2^2
KEi = KEf
0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2
0.5*m1*(u1^2-v1^2) = 0.5*m2*(v2^2-u2^2).....(2)
solving 1&2
we get
u1 + v1 = v2 + u2
u1 - u2 = v2-v1
v2 = u1 - u2 + v1 ..........(3)
using 3 in 1
v1 = ((m1-m2)*u1 + (2*m2*u2))/(m1+m2)
v2 = ((m2-m1)*u2 + (2*m1*u1))/(m1+m2)
speed of first ball v1 = ((m-m)*1.25-(2*m*1.15))/(m+m) = -1.15 m/s
speed of second ball v2 = (-(m-m)*1.15+(2*m*1.25))/(m+m) = 1.25 m/s
=====================
2)
thrower
initial momentum pi = (68+0.05)*2.2
final momentum Pf = (68*v) + (0.05*33)
from momentum conservation
Pf = Pi
(68*v) + (0.05*33) = (68+0.05)*2.2
v = 2.1773 m/s <<<----------answer
catcher
initial momentum Pi = 59*0
final momentum Pf = (59+0.05)*vf
Pf = pi
vf = 0 <<<<----answer
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