PHYSICS 103: Lecture 7 Review HW Solutions Applications of Newton’s Laws  Air resistance  Friction  Ramps  Example problems Agenda for Today:

N EWTON’S L AWS OF M OTION FIRST LAW FIRST LAW: An object at rest will remain at rest and an object in motion will remain in motion unless acted upon by an external force. SECOND LAW SECOND LAW: The net force on an object is equal to the product of that object’s mass times its acceleration. The acceleration is in the same direction as the force. F = m. a THIRD LAW THIRD LAW: For every force that one object exerts on a second object, there is an equal but oppositely directed force that the second object exerts on the first object.

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. The force of air resistance R acting on a sky diver increases as the velocity increases. R gets larger as the velocity increases If R=W then you don’t accelerate => you reach terminal velocity

Question: A man and a woman are parachuting from the same altitude. If the man is twice as heavy as the woman, and they have identical parachutes, who gets to the ground first? Question: A skydiver jumps from a helicopter. As she falls faster and faster through the air, does her acceleration increase, decrease, or remain the same? Test your understanding

Question: When I slide a block across a table, why does it come to a stop? FRICTION

Opposes relative motion of two surfaces Acts to bring two surfaces to one velocity Is a reactionary force Comes in two kinds : static and sliding All surfaces are not perfectly flat

F RICTION NO Friction Static Friction Kinetic Friction FNFN FgFg FFfFf Sliding or Kinetic Friction: -acts to stop objects that are already sliding - forces have a fixed magnitude Static Friction: -acts to prevent objects from starting to slide - -forces vary from zero to an upper limit

FRICTION Increases: When you push surfaces more tightly together When you make surfaces rougher Static Friction: F f =  s F N Kinetic Friction: F f =  k F N  k <  s Peak static force is greater than sliding force

Why is it hard to move forward in your car on ice? Why does sand on ice help? Would you rather be in a porsche or buick in snow storm? Does skidding make you come to a stop faster or slower? How do anti-lock brakes work? Test your understanding

FNFN FgFg Ramps Why can you lift a very heavy object with a ramp? Why is it easier to lower an object than raise it? Why is it more difficult to ride a bike up a steep slope than a more gradual one? FNFN  FgFg FfFf

We already learned that when all forces balance there is no motion Unbalanced forces induce acceleration

Forces on a ramp  FgFg  F g sin  F g cos  F N = F g cos  a // = g sin 

  FgFg F g sin  F g cos  F N = F g cos  a // = g sin  Question: What is the acceleration of a 30 kg block sitting on a frictionless ramp with a 30 degree incline if I apply a 200 N force along the ramp? We know: m = 30 kg F g = mg = 30 (9.8) N = 294 N a = F net /m = 53/30 m/s 2 = 1.77 m/s 2

Example Problems Distributed in Class: Test your understanding

Main Points from Today’s Lecture Applications of Newton’s Laws  Air resistance You should understand that there is a force acting against gravity causing your acceleration to be less than g. This force increases with velocity until it equals your weight. You then reach terminal velocity  Friction You should understand that friction is a reactionary force that opposes motion. It comes in two kinds (static and kinetic) and it is a function of how rough a surface is and the normal force.  Ramps You should understand how to find the net force on an object on a ramp to find the acceleration  Example problems