Physics 151 Week 9 Day 1 Topics: Work, Energy, & Newton’s 2nd Law  Energy and Work  Force and Motion Graphs Questions from last time  Net force vs. acceleration  Mass vs. Acceleration  Applying Newton’s 2nd Law  Apparent Weight  Brainstorm: What do we know about friction? Wednesday’s Class: All about Forces & friction

Slide 10-3

Slide 10-4

Forms of Energy Mechanical Energy Thermal Energy Other forms include Slide 10-12

The Basic Energy Model Slide 10-13

Energy Transformations Kinetic energy K = energy of motion Potential energy U = energy of position Thermal energy E th = energy associated with temperature System energy E = K + U + E th + E chem +... Energy can be transformed within the system without loss. Energy is a property of a system. Slide 10-14

Some Energy Transformations E chem  U g K  E th E chem  U g U s  K  U g Slide 10-15

Energy Transfers These change the energy of the system. Interactions with the environment. Work is the mechanical transfer of energy to or from a system via pushes and pulls. Slide 10-20

Energy Transfers: Work W  KW  E th W  U s Slide 10-21

The Work-Energy Equation Slide 10-22

Work Slide 10-28

Work Done by Force at an Angle to Displacement Slide 10-29

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. 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

Constant Force Model Slide 4-19 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

Net Force and Motion Graphs

Net Force vs. Acceleration Graphs

Net Force vs. Mass Graphs

Reading Quiz 1.Which of the following statements about mass and weight is correct? A.Your mass is a measure of the force gravity exerts on you. B.Your mass is the same everywhere in the universe. C.Your weight is the same everywhere in the universe. D.Your weight is a measure of your resistance of being accelerated. Slide 5-5

Answer 1.Which of the following statements about mass and weight is correct? A.Your mass is a measure of the force gravity exerts on you. B.Your mass is the same everywhere in the universe. C.Your weight is the same everywhere in the universe. D.Your weight is a measure of your resistance of being accelerated. Slide 5-6

Example Problem A 100 kg block with a weight of 980 N hangs on a rope. Find the tension in the rope if A.the block is stationary. B.it’s moving upward at a steady speed of 5 m/s. C.it’s accelerating upward at 5 m/s 2. Slide 5-15

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

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

Friction Brainstorm One person in each team takes out a sheet of paper and records their group brainstorming everything they know about friction.

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/s 2 ? Do these answers have the expected behavior in the limit θ → 0° and θ → 90°? Example Problem Slide 5-28

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? Example Problem Slide 5-22