Topics: Newton’s 2nd Law and Applications Physics 151 Week 10 Day 3 Topics: Newton’s 2nd Law and Applications Applying Newton’s 2nd Law Nature of Friction Kinetic Friction Static Friction Coefficients of Friction

General Force Model Newton 0th Law Objects are dumb - They have no memory of the past and cannot predict the future. Objects only know what is acting directly on them right now Newton's 1st Law An object that is at rest will remain at rest and an object that is moving will continue to move in a straight line with constant speed, if and only if the sum of the forces acting on that object is zero. ax = 0 m/s2 IFF Sum Fx = 0 N (IFF => if and only if) Newton's 3rd Law Recall that a force is an interaction between two objects. If object A exerts a force on object B then object B exerts a force on object that is in the opposite direction, equal in magnitude, and of the same type. Visualizations: Force Diagrams System Schema

Net Force Model Newton's 2nd Law acceleration of an object = sum of forces acting on that object / the mass of the object Remainder of week: Friction Model Apparent Weight Slide 4-19

Rank the Forces Three identical bricks are pushed across a table at constant speed. The arrow pushes horizontally. (Note: there is friction between the bricks and the table.) Draw separate free-body diagrams for each of the systems A and B. Rank the magnitudes of all the horizontal forces that you identified above in order from largest to smallest. (Recall that the bricks are pushed so that they move at constant speed.)

Static & Kinetic Friction - Part I Slide 4-19

Static & Kinetic Friction Describe what is happening to the forces on the box and the effect of the forces on the motion of the box from the pictures. Slide 4-19

Static & Kinetic Friction - Part III Below is graph of the friction force exerted by the table on the box. 
 Label times a-f that match the free-body diagrams in the previous problem. If the mass of the box is 3.0 kg, the maximum Ffs is 10 N, and Ffk has an average of 6.0 N, find the coefficients of static and kinetic friction. Slide 4-19

Coefficients of Friction What can you deduce/generalize about friction forces from this table? Describe 3-4 real world situations that can be explained by this table Slide 4-19

Clicker Question The coefficient of static friction is smaller than the coefficient of kinetic friction. equal to the coefficient of kinetic friction. larger than the coefficient of kinetic friction. equal to or larger than the coefficient of kinetic friction not discussed in this chapter. Answer: C Slide 5-9

Answer The coefficient of static friction is smaller than the coefficient of kinetic friction. equal to the coefficient of kinetic friction. larger than the coefficient of kinetic friction. equal to or larger than the coefficient of kinetic friction not discussed in this chapter. Answer: C Slide 5-10

Parking on a Hill If you park on a hill with a 10 degree slope with the car held by the parking brake, what is the magnitude of the frictional force that holds your car in place? The coefficient of static friction between your car's wheels and the road when wet is 0.30. What is the largest angle slope on which you can park your car in the rain so that it will not slide down the hill? The coefficient of kinetic friction between your wheels and the wet road surface is 0.25. If someone gave your your car a push on the wet hill and it started sliding down, what would its acceleration be? Slide 4-19

Example Problem A sled with a mass of 20 kg slides along frictionless ice at 4.5 m/s. It then crosses a rough patch of snow which exerts a friction force of 12 N. How far does it slide on the snow before coming to rest? Slide 5-21

Example Problem A 75 kg skier starts down a 50-m-high, 10° slope on frictionless skis. What is his speed at the bottom? Slide 5-27

Example Problem Burglars are trying to haul a 1000 kg safe up a frictionless ramp to their getaway truck. The ramp is tilted at angle θ. What is the tension in the rope if the safe is at rest? If the safe is moving up the ramp at a steady 1 m/s? If the safe is accelerating up the ramp at 1 m/s2? Do these answers have the expected behavior in the limit θ → 0° and θ → 90°? Slide 5-28

Example Problem Macie pulls a 40 kg rolling trunk by a strap angled at 30° from the horizontal. She pulls with a force of 40 N, and there is a 30 N rolling friction force acting on trunk. What is the trunk’s acceleration? Slide 5-22