Momentum and Impulse Momentum (p) ◼ All moving objects have momentum. ◼ The momentum of a moving object can be determined by multiplying the object’s mass and velocity. ◼ Momentum = Mass x Velocity Momentum ◼ Momentum: motion” ◼ Variable: “the quantity of p momentum = mass x velocity p = mv ◼ Units: kg.m/s Momentum ◼ Like velocity, acceleration, and force, momentum is described by its direction as well as its quantity (vector). ◼ The momentum of an object is in the same direction as its velocity. Momentum The more momentum a moving object has, the harder it is to stop. ◼ The mass of an object affects the amount of momentum the object has. ◼ For example, you can catch a baseball moving at 20 m/s, but you cannot stop a moving car at the same speed. ◼ Momentum The car has more momentum because it has a greater mass. ◼ The velocity of an object also affects the amount of momentum an object has. ◼ For example, an arrow shot from a bow has a large momentum because, although it has a small mass, it travels at a high velocity ◼ Momentum Objects which aren’t moving have no velocity, and therefore no momentum. ◼ The faster a body moves, the larger its momentum. A heavy object moving with a certain velocity has more momentum than a light object moving with the same velocity. ◼ Sample Momentum Problems ◼ Which has more momentum: a 3kg hammer swings at 1.5m/s, or a 4kg hammer swings at 0.9m/s? Sample Momentum Problems ◼ Which is harder to stop: an 80-kg man running at m/s, or a 1000-kg truck moving at 1m/s? Impulse (J) ◼ Impulse: The change in momentum of an object due to a force that is applied during a period of time impulse = force x time J = Ft ◼ Units: N.s (kgm/s) Impact ◼ ◼ Impact- The time duration in which a change in momentum is occurring. Units- seconds When does change in momentum happen? ◼ When the mass changes. ◼ When the speed changes. (slow down, speed up, stopped) ◼ When the direction of motion changes. Impulse-Momentum Relationship ◼ Impulse is equal to a change in momentum J = Dp or Dp = 𝑝𝑓 - 𝑝𝑖 = 𝑚𝑣𝑓 - 𝑚𝑣𝑖 or Dp = m(𝑣𝑓 - 𝑣𝑖 ) Sample Problems 1. A. B. A 56.6 – g tennis ball is initially moving with a velocity of 22.2 m/s to the right toward the racket. After bring hit by the racket, the ball rebounds and begins to move to the left at 27.8 m/s. If the ball and the racket are in contact for 0.005 second, calculate the change in momentum of the ball The force that the racket exerts on the ball A. What is impulse (change in momentum)? B. How much force did the racket exert on the ball to change its momentum? Vf 27.8 m/s 22.2 m/s Vi ball’s mass =56.6 – g (0.0566kg) time of impact 0.005 s Sample Problems 2. A net force of 25 newtons is applied to a 20 – kg cart for 2 seconds. A. B. What is impulse (J)? What is the change in momentum (Dp)? Sample Problems 2. A net force of 25 newtons is applied to a 20 – kg cart for 2 seconds. A. B. What is impulse (J)? What is the change in momentum (Dp)? Sample Problems 3. A 50 – kg object is sitting on a frictionless surface. An unknown constant force pushes the object for 2 seconds until it reaches a velocity of 3 m/s. A. What is the initial momentum of the object? B. What is the final momentum of the object? C. What was the force acting on the object? D. What was the impulse acting on the object? Forces of Impact •Forces of impact are reduced when time of impact increases Forces of Impact ◼ Forces of impact are also reduced when: ◼ the velocity of impact is reduced ◼ the mass of the object is reduced Time of Impact ◼ The time of Impact affects the amount of force in the collision. Do this! In 2011, Ivo Karlovic of Croatia served a tennis ball at a speed of 251 kph. If the mass of the ball was 57 grams, and assuming that the ball had zero initial velocity along the horizontal and that its final velocity was along the horizontal, calculate how much impulse was needed to achieve this serve. Getting the Total Momentum of a System ◼ Alex and Russell are riding their bicycles side by side on the sidewalk. The total mass of Alex and his bike is 80kg; the total mass of Russell and his bike is 90kg. If they are both moving at a speed of 5.5m/s, what is their total momentum? Getting the Total Momentum of a System 𝑃𝑡 = 𝑚1 𝑣1 + 𝑚2 𝑣2 5.5 m/s Alex 80 kg 5.5 m/s Russell 90 kg Getting the Total Momentum of a System ◼ Now let’s assume that Alex is riding his bike at 5.5 m/s westward and that Russell is riding his bike eastward at 5.5 m/s. What is their total momentum? Getting the Total Momentum of a System 𝑃𝑡 = 𝑚1 𝑣1 + 𝑚2 𝑣2 5.5 m/s 5.5 m/s 90 kg 80 kg Russell Alex Getting the Total Momentum of a System 𝑃𝑡 = 𝑚1 𝑣1 + 𝑚2 𝑣2 Calculate the total momentum of each pair of the objects below 1 m/s 2 m/s 1 kg 2 kg 1 m/s 2 m/s 3 kg 1 kg 𝑃𝑡 = 𝑚1 𝑣1 + 𝑚2 𝑣2 Calculate the total momentum of each pair of the objects below 1 m/s 2 m/s 2 kg 2 kg 1 m/s 3 kg 1 m/s 3 kg COLLISIONS ◼ ◼ ◼ ◼ ◼ Billiard ball hitting another on the table A car crashing into another car An asteroid striking a planet A cue stick hitting a ball A baseball bat hitting a ball TYPES OF COLLISION ◼ Elastic ◼ Inelastic ELASTIC COLLISION An elastic collision results when two elastic bodies collide ◼ When two bodies collide then separate afterwards ◼ Examples: ➢ Collision between billiard balls ➢ Collision between ball and bat ➢ Tennis ball and racket ➢ Collision between atoms ◼ INELASTIC COLLISION When two bodies collide and stick together after the collision ◼ Examples: ➢ A car crashed with another car ➢ A car crashing against the tree ➢ A gum thrown on to the wall ➢ A dropped ball of clay doesn’t rebound ◼ COLLISION DEPENDS ON MATERIALS Whether the collision between two objects is elastic or inelastic depends on the materials that make up the objects. ◼ Recall that an elastic material is capable of being temporarily deformed by forces and returning to its original size and shape once the forces are removed. ◼ Conservation of Momentum In everyday language, conservation means saving resources. ◼ The word conservation has a more specific meaning in physical science. ◼ In physics, conservation refers to the conditions before and after some events. ◼ The total momentum of objects have is conserved when they collide. ◼ Conservation of Momentum Momentum may be transferred from one object to another, but none is lost. This fact is called the Law of Conservation of Momentum. ◼ The law states that, in the absence of outside force, the total momentum of objects that interact does not change. ◼ Conservation of Momentum ◼ The amount of momentum is the same before and after they interact. 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃𝑖 = 𝑃𝑓 𝑚1 𝑣1 + 𝑚2 𝑣2 = 𝑚1 𝑣1′ + 𝑚2 𝑣2′ Law of Conservation of Momentum In the absence of an external force, the momentum of a system does not change. Elastic Collisions Inelastic Collisions ◼ When colliding objects stick together and travel off as one object ◼ For two objects in an inelastic collision: momentum1 + momentum2 = combined momentum1&2 m1v1 + m2v2 = (m1 + m2)vf Inelastic Collisions Bell Ringer 10/18 One pool ball traveling with a velocity of 5 m/s hits another ball of the same mass, which is stationary. The collision is head on, as momentum is conserved, and they bounce off each other. What type of collision is this? What are the final velocities of both bodies? ◼ A 0.150-kg baseball moving at a speed of 45.0 m/s crosses the plate and strikes the 0.250-kg catcher's mitt (originally at rest). The catcher's mitt immediately recoils backwards (at the same speed as the ball) before the catcher applies an external force to stop its momentum. Determine the post-collision velocity of the mitt and ball. Bell Ringer ◼ Two meatballs are speeding directly toward each other. One is a 4.0-kg meatball moving with a speed of 6.0 m/s, and the other has a mass of 2.0 kg and a speed of 4 m/s. If they collide inelastically, what will be the speed of the resulting 6.0 kg meatball immediately after the collision? Review Question ◼ A bullet with a mass of 0.020 kg collides inelastically with a wooden block of mass 2.5 kg, initially at rest. After the collision, the bullet + block has a speed of 1.2 m/s. What was the initial speed of the bullet? 
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