PHY 102 1st Edition I First law of motion a Newton s first law b Law c Aristotle II Questions III Types of Forces IV Where Aristotle went wrong V Momentum and Inertia Outline of Current Lecture Current Lecture I Conservation of momentum the momentum before a collision is the same as the momentum after a collision a Experiment demonstrating the velocity of an object after a collision i Remember that momentum has direction and is mass velocity ii Two carts are placed on a track and will collide in between two monitors of each cart s velocity iii Momentum before 1 kg 3 m s and p mv so M 3 kg m s iv Momentum after m1 m2 2 kg and Vf 1 5 m s and p mv so M 3 kg m s v Pi Pf b Example These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute i m1 kg and m1 m2 1 1 2 kg Vi 3 4 m s 3 4 m s 85 kg m s So we know the end result needs to be 85 kg m s because momentum is equal after the collision SO 85 kg m s 1 5 kg Vf Vf 85 kg m s 1 5 kg 567 m s II Numerical problems a A truck with a mass of 3 000 kg and a velocity of 20 m s collides head on with a car of 1500 kg and a velocity of 20 m s If the vehicles stick together what is the resulting motion of the pair We know pi pf m1 m2 V V m1 v 1 m2 v 2 m1 m2 3000 kg 20sm 1500 kg 20s m 3000 kg 1500 kg 30 000 m s 4500 b Two dynamic carts are separated by a compressed spring The mass of cart 1 is twice the mass of cart 2 That is m1 2m2 The spring is released and the carts fly apart If cart 1 has a velocity of 3 m s what is the velocity of cart 2 pi pf 0 m1 v1 m2 v2 m1 v1 m2 v2 2v1 v2 v2 6 m s TEST QUESTION If two carts that start at 0 momentum and they roll away from each other and one cart has a momentum of 100 what is the momentum of the other cart ANSWER 100 c A train car mass 11 200 kg is moving along at a speed of 2 m s A 5 000 kg mass of coal with no horizontal motion is dropped into the hopper of the train car What is the resulting motion of the train car now loaded with coal i p1 pf mtrain vtrain mcoal mtrain V V mtrain vtrain mcoal mtrain 11 200 2 m s 5000 11 200 kg 1 38 m s TEST QUESTION What is the momentum of a pen in someone s hand ANSWER 0 But before it hits a table when dropped it has momentum How is this possible The mass of the whole world is too large to account for in the equation III Newton s Second Law a The net instantaneous force acting on an object is precisely the instantaneous change of its momentum per unit time IN symbols the second law can be written as F delta P delta T with delta T being very small b Note that F and delta P are vectors c Experiment cart is released on a track and acceleration is charted as mass of the system is constant but weights are moved from one side of the track to a force on the cart Acceleration Force 3 4 50 7 36 100 13 3 150 15 5 200 Acceleration is proportional to the force Then the experiment is redone by adding the weights to the cart to increase the mass Acceleration Mass 7 18 550 5 40 650 4 34 750 3 64 850 Acceleration is inversely proportional to the mass F ma IV Second Law Reprise a F delta P delta T b F delta mv delta T c F m deltaV delta T d F ma e Both F and a are vectors m is a scalar f g The sum of forces acting on a body produce an acceleration inversely proportional to mass F ma where F is expressed in Newtons Weight mg What is the weight of a person with a mas of 81 kg Note that g 9 8 m s 2 81 kg 9 8 m s 2 793 8 N