2D Collisions Physics 12 Adv

2D Collisions In all collisions, momentum is conserved In elastic collisions, kinetic energy is also conserved As momentum is a vector, we can break momentum into components and employ the conservation of momentum

2D Collision Two cars approach an intersection; the first car is travelling east at a velocity of 15m/s and the car has a mass of 1000.kg. The second car is travelling north at a velocity of 10.m/s and has a mass of 1200.kg. If the cars collide and stick together, determine the following: The velocity immediately after the collision The direction of motion immediately after the collision

2D Collision v=15m/s v=? A A B v=10.m/s B

2D Collisions

Elastic Collisions A proton travelling with speed 8.2x105m/s collides elastically with stationary proton in a hydrogen target. One of the protons is observed to be scattered up at a 60.° angle. At what angle will the second proton be scattered? What will the speed of each of the protons be after the collision?

Elastic Collisions v’1= ? 1 v1= 8.2x105m/s 1 2 2 v’2=? Before After

Kinetic Energy

Momentum

Three Equations, Three Unknowns

In Equations 2 and 3, take v’1 to left and square both sides

Add the final steps from the last step then substitute equation 1

Use the answer for v’1 to solve for v’2 and angle

Ballistic Pendulum In a ballistic pendulum, there are components where energy is conserved and components where it is lost It is therefore important that we analyze each component of the system correctly

Inelastic Collision The first part of the analysis involves the inelastic collision between the projectile and the bob We know that as it is an inelastic collision, momentum is conserved but energy is not

Pendulum After the collision, the projectile and bob act as a pendulum and will swing to a maximum height If this height can be measured, then through the conservation of energy, we can determine the speed of the projectile and bob immediately after the collision

Question A forensic expert needed to find the velocity of a bullet fired from a gun in order to predict the trajectory of a bullet. She fired a 5.50g bullet into a ballistic pendulum with a bob that had a mass of 1.75kg. The pendulum swings to a height of 12.5cm above its rest position before dropping back down. What was the velocity of the bullet before it hit and became embedded in the bob?

Analysis

Analysis

Practice Problems Page 509 Page 515 Page 524 Questions 35-37