Unformatted text preview: Chapter 7
Linear Momentum Momentum (p) the product of a object's mass and velocity.
A measure of how difficult it is to stop a moving object. Inertia of motion (Newton: "quantity of motion") p = mv Momentum Newton's Second Law: the net force on an object is equal to the rate at which its momentum p F = changes. t Newton's Second Law in terms of momentum can be rewritten as: Momentum and Impulse
Ft = p or Ft = mv Impulse (Ft) A force exerted over a period of time.
The force during a collision usually varies so we must consider the average force. The force felt during a collision is reduced if the time for the collision to occur is increased. Example: car safety devices, "rolling with the punches" Momentum and Impulse Example: A 1400 kg car traveling west at 15 m/s collides with a utility pole and is stopped in 0.3 seconds. Find the impulse imparted on the car and the force on the car during the collision. Example (Happy/Sad Demo): Two wrecking balls have the same mass and move at the same velocity toward the same wall. One is made of an elastic material and bounces back when it strikes the wall, the other is made of an inelastic material and sticks to the wall. In which case the impulse the greatest? Conservation of Momentum Law of Conservation of Momentum: "The total momentum of an isolated system of objects remains constant." Types of interactions: 1. Elastic collision objects hit and bounce off pbefore = pafter No energy is lost in the collision Both momentum and kinetic energy are conserved. Combining with KE equation gives:v - v = - v
1 2 ( 1 - v2 ) Examples: billiard balls, collisions between gas molecules Types of interactions: 2. Inelastic collision objects hit and stick together. Conservation of Momentum 3. Explosion At least some KE is lost in the collision Only momentum is conserved, KE is not. Examples: train cars coupling, car wreck where the two cars become entangled. Beginning momentum and KE is zero. Momentum is conserved, but KE is not. Examples: Gun recoil, rocket propulsion Conservation of Momentum Example: A 5.0 kg bowling ball moving to the right at 4.0 m/s collides elastically with a 3.0 kg ball moving to the left at 3.0 m/s. Find the velocity of the two balls after the collision. Show that KE is conserved. Example: A 1000 kg train car moving East at 10 m/s collides and connects with a 2000 kg train car moving at 20 m/s to the West. What is the velocity of the cars after the collision? How much KE was lost in the collision? Example: A 25 g bullet is fired from a 4 kg rifle. Find the recoil velocity of the rifle if the muzzle velocity of the bullet is 250 m/s. Conservation of Momentum Example: The Ballistic Pendulum A bullet (m=0.050 kg) moving at 200 m/s strikes and becomes embedded in a 3.5 kg block of wood hanging stationary from a string. How high does the bullet/block swing after impact? Collisions in 2 Dimensions It is possible use momentum to approach problems that occur in 2 (or even 3) dimensions. Treat the momentum as a vector that can be resolved into its x and y components. Momentum in both directions (x and y) is conserved. Collisions in 2 Dimensions Example: A 500 kg car is moving east at 15 m/s when it collides with a 700 kg car moving north at 10 m/s. What is the velocity (speed and direction) of the two cars if they become entangled after the collision? Example: A cue ball moving at 3 m/s strikes another stationary billiard ball with equal mass. After the collision, the cue ball moves at 1.8 m/s at an angle of 30 degrees to its original path. What is the velocity (speed and direction) of the other ball? Thus far, we have approximated real, extended objects as points or particles that can only undergo translational (linear) motion. Center of Mass/Center of Gravity Point of application of a force does not matter. However, real extended objects are NOT points and can undergo other types of motion, such as rotational. Point of application of a force DOES matter. Center of Mass (CM) point on an extended object that will follow the same path as a particle exposed to the same net force. Center of Mass/Center of Gravity Center of Gravity (CG) point on an object where the force of gravity can be considered to act. Point where all the mass of an object can be considered to be concentrated. very similar to the CM and for almost all cases is at the same location on an object or system of objects. Point about which an extended object will freely rotate. Important for balance and stability of extended objects. Center of Mass/Center of Gravity An object will tip over if its CM lies beyond its base of support (why a low CG is advantageous for stability). Can be found for a single extended object or for a system of several objects. Ex: The CM of the Earth/ Moon system orbits the Sun Depends on the mass and distribution of the object or objects. Center of Mass/Center of Gravity Location of the CM for an extended object can be found experimentally by hanging an object from two different pivot points. The CM will always lie on a vertical line directly below the pivot point. xposition of the CM for a system of objects is found by: m x + m x + xCM = 1 1 2 2 m1 + m2 Example: Find the CM of the Earth/Moon system. Example: Three people of roughly equal mass sit along a lightweight banana boat at distances of 1.0m, 5.0m, and 6.0 m from one end. Find the position of ...
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