PHY 102 1st Edition Exam 2 Study Guide Lecture 10 September 18 Position the magnitude and direction from an arbitrary location Difference between distance and displacement distance is the track along which something travels and the displacement is the straight line distance between the beginning and end point Example blue is distance and black is displacement Vector magnitude and direction Measurements include velocity acceleration displacement momentum force change in momentum Velocity speed direction Important equations to note o V v1 vt Acceleration rate in change of velocity speed or direction Relationships in positive and negative acceleration o If v and a the object goes faster in the direction o If v and a the object goes slower in the direction o If v and a the object goes slower in the direction o If v and a the object goes faster in the direction Acceleration is in the same direction as the force Remember that negative acceleration does not necessarily mean slowing down Do not use the term deceleration One example from this lecture a A vehicle accelerates from rest to 22 m s in 4 s A V0 0 m s V 22 m s T 4s V v0 at v v0 at a v v0 t a 22 m s 0 4 a 5 5 m s2 Newton s First Law A body at rest will stay at rest and a body in motion will stay in motion with constant velocity along a straight line when not acted upon by external forces i e friction The first law is also a specific case of the second law in which the acceleration is 0 Important misconception objects do not need a constant source of force to keep them in the same state of motion unless in the presence of friction o Forces that act upon an object in motion External Friction Sound loss Example questions o When an object is moving with a fixed velocity is it accelerating A No o When an object is moving with a fixed speed is it accelerating A Maybe If there is a change in direction then the answer is yes o If a car is moving at a constant speed of 60 mph as it turns a corner is it accelerating A Yes Aristotle s Mistakes Motion is a natural state for a body not just rest The air is carried along with the spinning earth Concepts of Projectile motion o A projectile is not left behind because it has forward motion of its own o When something is moving forward it shares in the forward motion Momentum p p mv units typically in Newtons or kg m s Conservation of momentum the momentum is the same before and after a collision o EXAMPLE Two carts are placed on a track and will collide in between two monitors of each cart s velocity Momentum before 1 kg 3 m s and p mv so M 3 kg m s Momentum after m1 m2 2 kg and Vf 1 5 m s and p mv so M 3 kg m s Inertia is proportional to mass not a numerical value Most important to remember Pi Pf initial momentum equals final momentum o EXAMPLE 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 Newton s Second Law The net instantaneous force acting upon an object is precisely the instantaneous change of its momentum per unit of time The second law is written as F P T Important concepts to note o Acceleration is proportional to force o Acceleration is inversely proportional to mass F ma Equations to represent Newton s Second Law P o F T o F mv t o F m v t o F ma o F ma EXAMPLE A car with the mass of 1500 kg accelerates at a rate of 2 m s 2 under a constant force What are the magnitude and direction of that force F ma Force M 1500 kg A 2 m s2 F 1500 kg 2 m s2 3000 N Another example N kg m s2 o A force of 7 N is applied to a 3 5 kg mass for 2 seconds What is the change of velocity F ma F 7N F m v t v M 3 5 kg T 2s v 7 0 N 2 s 3 5 kg 4 m s Newton s Third Law If an object A exerts a force Fab on an object B then object B exerts a force Fba on object A such that Fab Fba The sum of the two forces vectors have to be 0 because the object is not accelerating In this event of a collision the masses of the vehicles are very different but the forces will be equal Large mass small mass The change in velocity will be less in the large truck because it has a larger mass so the passenger will likely survive A greater mass for a given force gives lesser acceleration the same force applied to two different masses gives different results Forces are equal in the event of a collision Weight the force of gravity upon an object Remember that the acceleration of gravity in free fall is 9 81 m s2 Here is a demonstration of Newton s Third Law in relation to weight 740 N 740 N Weight of the person Force of the earth on the person Example theory question Does the weight of an object at rest change Yes The mass is constant but the force of gravity changes