Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collid
ID: 1449748 • Letter: T
Question
Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide with a glancing blow. Asteroid A, which was initially traveling at vA1 = 40.0 m/s with respect to an inertial frame in which asteroid B was at rest, is deflected 30.0 from its original direction, while asteroid B travels at 45.0 to the original direction of A, as shown in (Figure 1) .
a) Find the speed of asteroid A after the collision.
b) Find the speed of asteroid B after the collision
c)What fraction of the original kinetic energy of asteroid A dissipates during this collision?
Explanation / Answer
from the law of conservation of linear momentum
A)p=40m where m is any arbitrary mass
you know that this linear momentum must be conserved after the collision so the combined momentum of the two rocks after should equal this amount. Set up a system of equations using the components of each momentum
x direction
40m=mv(a)cos30+mv(b)cos(-45)
40=v(a)cos30+v(b)cos(-45)
this is the total momentum in the x-direction.
so lets take the y components :
it initially has no momentum in the y direction so
0=v(a)sin30+v(b)sin(-45)
0.5v(a)-0.7071v(b)=0
0.8660v(a)+0.7071v(b)=40
you can add these two equations to solve for v(a) and you get
1.366v(a)=40
v(a)=29.3 m/s
B)plug this in to either equation to get v(b)= 20.7 m/s
C)find the kinetic energy of the original asteroid and the kinetic energy of the two final asteroids added together.
so initial kinetic energy is
1/2mv^2= 0.5m(40)^2
and final kinetic is =0.5m(29.3)^2+0.5m(20.7)^2
800m for initial
429.245+214.245= 643.49 for final
you need to find the fraction lost so subtract and get
800-643.49= 156.51
find out what percent of the original this amount is
156.51/800=.196 or 19.6%