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MOMENTUM Momentum: LINEAR a vector quantity defined as the product of an objects mass and velocity Momentum describes an objects motion p = mv The direction of the momentum is the direction of the velocity. The SI units are kilogram-meters per second (kg-m/s) IMPULSE A change in momentum takes force and time. Impulse: for a constant external force, the product of the force and the time over which it acts on an object. F t = p = m(vf v0) In soccer for example: when the ball is moving very fast the player must exert a large force over a short time to change the balls momentum and quickly bring the ball to a stop. Stopping times and distances depend on the impulse-momentum theorem. A change in momentum over a longer time requires less force. AN ANALOGY A mood is something you have you are happy, sad, angry, etc. it is a characteristic of your current state of being. In the same way, momentum is something that an object has it is a characteristic of its current physical state. A pop quiz in physics is something that happens to you. In the same way, an impulse is something that happens to an object. Just like a pop quiz in physics can affect your mood, an impulse will affect the momentum of an object IMPULSE RIDING WITH THE PUNCH AND IMPULSE REAL WORLD APPLICATIONS OF IMPULSE REBOUNDING MOMENTUM QUESTIONS If the speed of a particle is doubled A) by what factor is its momentum changed? B) What happens to its KE? A pitcher claims he can throw a 0.145 kg baseball with as much momentum as a speeding bullet. Assume that a 3 g bullet moves at a speed of 1,500 m/s. A)What must the baseballs speed be if the pitchers claim is valid? B) Which has greater KE, the ball or the bullet? ANSWERS A) p 2 x B) KE 4 x mbb = 0.145 kg mb = 0.003 kg vb = 1500 m/s vbb = ? Mbbvbb = mbvb (0.145 kg)vbb =(0.003 kg)(1500 m/s) vbb = 31 m/s KEbb = (0.145 kg)(31 m/s) 69.7 J KEb = (0.003 kg)(1500 m/s) 3375 J The bullet has more KE MOMENTUM IS CONSERVED The total momentum of all objects interacting with one another constant regardless remains of the nature of the forces between the objects. m1v1,0 + m2v2,0 = m1v1,f + m2v2,f Momentum is conserved in collisions and for objects pushing away from each other. CONSERVATION OF MOMENTUM NEWTONS 3RD LAW Newtons third law leads to conservation of momentum. Remember: for every action there is an opposite but equal reaction However, in reality forces in real collisions are not conserved (constant). NEWTONS 3RD LAW AND CONSERVATION OF MOMENTUM CONSERVATION OF MOMENTUM CONSERVATION QUESTIONS A 44 kg student on in-line skates is playing with a 22 kg ball. The student is holding the ball, and both are at rest. The student then throws the ball horizontally, causing the student to glide back at 3.5 m/s. (Disregard friction)What is the velocity of the ball? The same student is initially at rest and then catches the ball, which is initially moving to the right at 4.6 m/s. (Disregard friction) What is the velocity of the student? ANSWERS (ms + mb)(v0,s + b) = ms(vf,s) + mb(vf,b) 0 = (44kg)(-3.5 m/s) + (22 kg)(vf,b) Vf,b = 7 m/s forwards (ms)(v0,s) + (mb)(v0,b) = (ms + mb)(vf,s + b) 0 + (22 kg)(+4.6 m/s) = (44 kg + 22 kg)(vf,s + b) vf,s + b = 1.53 m/s right TYPES OF COLLISIONS INELASTIC COLLISIONS Perfectly inelastic collision: a collision in which two objects stick together and move with a common velocity after colliding. m1v1,0 + m2v2,0 = (m1 + m2)vf The total momentum of the two objects before the collision is the same as the total momentum of the two cars after the inelastic collision. Kinetic energy is not constant in inelastic collisions. ELASTIC COLLISIONS Elastic collision: a collision in which the total momentum and the total kinetic energy remain constant. In an elastic collision, two objects collide and return to their original shapes with no change in total kinetic energy. After the collision, the two objects move separately. m1v1,0 + m2v2,0 = m1v1,f + m2v2,f m1v1,0 + m2v2,0 = m1v1,f + m2v2,f Most collisions are neither elastic nor perfectly inelastic. ... View Full Document