C HAPTER 9 Momentum and Its Conservation

W HAT ’ S THE RELATIONSHIP BETWEEN FORCE AND VELOCITY ? What happens when the baseball is struck by the bat? _______________tells us that the forces on the bat and ball are equal. _______________tells us that both bat and ball will experience an acceleration proportional to their masses. But what is the relationship between the velocities of the ball and the bat and the forces they experience?

“T HE B IG M O ”: M OMENTUM The ________________ of an object of mass m moving with a velocity is defined as the __________ of the ______ and the __________. SI Units are kg m/s ( Dimensions = ML/T ) Vector quantity, the direction of the momentum is the same as the velocity’s.

M ORE A BOUT M O Momentum components: p x = m v x and p y = m v y Applies to two-dimensional motion. Again the direction of momentum and velocity are the same. Momentum is related to ________________. We can derive an equation that relates KE and momentum. More on kinetic energy in chapter 10.

C HANGING THE BIG MO How does an object change its acceleration? How would an object change its momentum? In order to change the momentum of an object, a _______________ must be applied.

I MPULSE The _________of change of momentum of an object is equal to the __________acting on it. Just like with acceleration, when the __________is zero, no change occurs to momentum. Gives an alternative statement of Newton’s second law.

I MPULSE When a single, constant force acts on the object, there is an ____________ delivered to the object. is defined as the impulse. ____________________, the direction is the same as the direction of the __________. The impulse is also described using the letter J. Impulse is useful for describing ______________ that do not last a long time. (More on this later.)

I MPULSE -M OMENTUM T HEOREM The theorem states that the ___________ acting on the object is equal to the ___________________ of the object. This theorem holds for _________ and ____________ forces. If the force is not constant, use the average force applied.

S AMPLE P ROBLEM Rico strikes a kg golf ball with a force of 272 N and gives it a velocity of 62.0 m/s. How long was Rico’s club in contact with the ball?

A VERAGE F ORCE IN I MPULSE The ______________can be thought of as the constant force that would give the same impulse to the object in the time interval as the actual time-varying force gives in the interval.

A VERAGE F ORCE AND COLLISIONS

I MPULSE AND COLLISIONS Impulse is most useful in describing _________ of _______________. The impulse-momentum theorem allows us to study the effects that the ________________of a collision has on the _________ felt by the ____________. For example, why is it important for boxers to wear boxing gloves?

C HANGING I MPULSE AND C OLLISIONS _____________ the contact time increases the ___________ but reduces the _________ during the collision. Increasing force increases the impulse as well.

I MPULSE A PPLIED TO A UTO C OLLISIONS The most important factor is the ___________or the time it takes the person to come to a rest. Increasing the collision time is the key factor. This will reduce the chance of dying in a car crash.

W AYS TO INCREASE THE TIME Crumple zones Air bags Seat belts

T YPICAL C OLLISION V ALUES For a 75 kg person traveling at 27 m/s and coming to stop in s. F = -2.0 x 10 5 N a = 280 g Almost certainly fatal: F = 90 kN fractures bone. a = 150 g for 4 ms causes spinal cord damage (causes the nerves to enter the base of the brain)

C OLLISIONS ______________ is conserved in any _________. ______________is not always conserved. Some KE is converted to other forms of energy (i.e. internal energy, sound energy, etc.) or is used to do the work needed to deform an object. Two broad categories of collisions: Elastic collisions Inelastic collisions: Perfectly inelastic and inelastic Elastic and perfectly inelastic collisions represent ideal cases of collisions. Most real world cases fit somewhere between these two extremes.

C ONSERVATION OF M OMENTUM Momentum in an isolated system in which a collision occurs is conserved. A collision may be the result of _______________ between two objects. “Contact” may also arise from the ______________ interactions of the electrons in the surface atoms of the bodies. An isolated system will have no external forces acting on the objects.

C ONSERVATION OF M OMENTUM The principle of conservation of momentum states when no external forces act on a system consisting of two objects that collide with each other, the total momentum of the system remains constant in time. Specifically, the total momentum before the collision will equal the total momentum after the collision. F

F ORCES IN A C OLLISION The force with which object 1 acts on object 2 is equal and opposite to the force with which object 2 acts on object 1. Impulses are also equal and opposite.

C ONSERVATION OF M OMENTUM FORMULA Mathematically: Momentum is conserved for the system of objects. The system includes _____________________ interacting with each other. Assumes only internal forces are acting during the collision. Can be generalized to any number of objects.

S AMPLE P ROBLEM A 1875 kg car going 23 m/s rear-ends a 1025 kg compact car going 17 m/s on ice in the same direction. The two cars stick together. How fast do the two cars move together immediately after the collision?

R ECOIL AND P ROPULSION IN S PACE Xe atoms are expelled from the ion engine. v atoms = 30km/h; F atoms = N Advantage: runs for a very long time

G LANCING C OLLISIONS For a general collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved. Use subscripts for identifying the object, initial and final velocities, and components. We will examine collisions in two-dimensions.

G LANCING C OLLISIONS The “after” velocities have x and y components. Momentum is conserved in the x direction and in the y direction. Apply conservation of momentum separately to each direction.

S AMPLE PROBLEM A 1,500 kg car traveling east with a speed of 25.0 m/s collides at an intersection with a 2,500 kg van traveling north at a speed of 20.0 m/s as shown in the figure. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision and assuming that friction between the vehicles and the road can be neglected.

C HAPTER 9 Momentum and Its Conservation THE END