6.4 CHAPTER 6. MOTIONIN TWO DIMENSIONS
What is the final velocity of each marble?SOLUTIONStep 1 : Decide how to approach the problem
We are given:- mass of marble 1, m 1 =50 g
- mass of marble 2, m 2 =100 g
- initial velocity of marble 1, vi 1 =0 m·s−^1
- initial velocity of marble 2, vi 2 =3 m·s−^1
- the collision is elastic
The masses need to be converted to SI units.
m 1 = 0, 05 kg
m 2 = 0, 1 kgWe are required to determine the final velocities:- final velocity of marble1, vf 1
- final velocity of marble2, vf 2
Since the collision is elastic, we know that - momentum is conserved, pi= pf.
- energy is conserved, KEi=KEf.
We have two equationsand two unknowns (v 1 , v 2 ) so it is a
simple case of solving aset of simultaneous equations.Step 2 : Choose a frame of reference
Choose to the right as positive.Step 3 : Draw a rough sketch of the situation(^2121)
Before Collision After Collision
m 2 = 100g
vi 2 = 3 m· s−^1
m 1 = 50g
vi 1 = 0
m 2 = 100g m 1 = 50g
Step 4 : Solve the problem