12.1 Momentum

Chapter 12 Objectives  Calculate the linear momentum of a moving object given the mass and velocity.  Describe the relationship between linear momentum and force.  Solve a one-dimensional elastic collision problem using momentum conservation.  Describe the properties of angular momentum in a system—for instance, a bicycle.  Calculate the angular momentum of a rotating object with a simple shape.

Chapter Vocabulary  angular momentum  collision  law of conservation of  momentum  elastic collision  gyroscope  impulse  inelastic collision  linear momentum  momentum

Inv 12.1 Momentum Investigation Key Question: What are some useful properties of momentum?

12.1 Momentum  Momentum is a property of moving matter.  Momentum describes the tendency of objects to keep going in the same direction with the same speed.  Changes in momentum result from forces or create forces.

12.1 Momentum  The momentum of a ball depends on its mass and velocity.  Ball B has more momentum than ball A.

12.1 Momentum and Inertia  Inertia is another property of mass that resists changes in velocity; however, inertia depends only on mass.  Inertia is a scalar quantity.  Momentum is a property of moving mass that resists changes in a moving object’s velocity.  Momentum is a vector quantity.

12.1 Momentum  Ball A is 1 kg moving 1m/sec, ball B is 1kg at 3 m/sec.  A 1 N force is applied to deflect the motion of each ball.  What happens?  Does the force deflect both balls equally?  Ball B deflects much less than ball A when the same force is applied because ball B had a greater initial momentum.

12.1 Kinetic Energy and Momentum  Kinetic energy and momentum are different quantities, even though both depend on mass and speed.  Kinetic energy is a scalar quantity.  Momentum is a vector, so it always depends on direction. Two balls with the same mass and speed have the same kinetic energy but opposite momentum.

12.1 Calculating Momentum  The momentum of a moving object is its mass multiplied by its velocity.  That means momentum increases with both mass and velocity. Velocity (m/sec) Mass (kg) Momentum (kg m/sec) p = m v

 You are asked for momentum.  You are given masses and velocities.  Use: p = m v  Solve for car: p = (1,300 kg) (13.5 m/s) = 17,550 kg m/s  Solve for cycle: p = (350 kg) (30 m/s) = 10,500 kg m/s  The car has more momentum even though it is going much slower. Comparing momentum A car is traveling at a velocity of 13.5 m/sec (30 mph) north on a straight road. The mass of the car is 1,300 kg. A motorcycle passes the car at a speed of 30 m/sec (67 mph). The motorcycle (with rider) has a mass of 350 kg. Calculate and compare the momentum of the car and motorcycle.

12.1 Conservation of Momentum  The law of conservation of momentum states when a system of interacting objects is not influenced by outside forces (like friction), the total momentum of the system cannot change. If you throw a rock forward from a skateboard, you will move backward in response.

12.1 Conservation of Momentum

12.1 Collisions in One Dimension  A collision occurs when two or more objects hit each other.  During a collision, momentum is transferred from one object to another.  Collisions can be elastic or inelastic.

12.1 Collisions

Elastic collisions Two kg billiard balls roll toward each other and collide head-on. Initially, the 5-ball has a velocity of 0.5 m/s. The 10-ball has an initial velocity of -0.7 m/s. The collision is elastic and the 10-ball rebounds with a velocity of 0.4 m/s, reversing its direction. What is the velocity of the 5-ball after the collision?

 You are asked for 10-ball’s velocity after collision.  You are given mass, initial velocities, 5-ball’s final velocity.  Diagram the motion, use m 1 v 1 + m 2 v 2 = m 1 v 3 + m 2 v 4  Solve for V 3 : (0.165 kg)(0.5 m/s) + (0.165 kg) (-0.7 kg)= (0.165 kg) v 3 + (0.165 kg) (0.4 m/s)  V 3 = -0.6 m/s Elastic collisions

Inelastic collisions A train car moving to the right at 10 m/s collides with a parked train car. They stick together and roll along the track. If the moving car has a mass of 8,000 kg and the parked car has a mass of 2,000 kg, what is their combined velocity after the collision?  You are asked for the final velocity.  You are given masses, and initial velocity of moving train car.

 Diagram the problem, use m 1 v 1 + m 2 v 2 = (m 1 v 1 +m 2 v 2 ) v 3  Solve for v 3 = (8,000 kg)(10 m/s) + (2,000 kg)(0 m/s) (8, ,000 kg) v 3 = 8 m/s The train cars moving together to right at 8 m/s. Inelastic collisions

12.1 Collisions in 2 and 3 Dimensions  Most real-life collisions do not occur in one dimension.  In a two or three-dimensional collision, objects move at angles to each other before or after they collide.  In order to analyze two-dimensional collisions you need to look at each dimension separately.  Momentum is conserved separately in the x and y directions.

12.1 Collisions in 2 and 3 Dimensions