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 EnergyMechanical Energy

Ug UsK

Thermal Energy

Eth

Other forms include

Echem Enuclear

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 Eth = energy associated with temperature

System energy E = K + U + Eth + Echem + ...

Energy can be transformed within the system without loss.

Energy is a property of a system.

Slide 10-14

Some Energy Transformations

Echem Ug K Eth

Echem Ug Us K Ug

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 K W Eth

W Us

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 LawObjects 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 LawAn 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 LawRecall 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 Lawacceleration of an object = sum of forces acting on that object / the mass of the object

Remainder of week:Friction ModelApparent Weight

Net Force and Motion Graphs

Net Force vs. Acceleration Graphs

Net Force vs. Mass Graphs

Reading Quiz1. 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

Answer1. 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 ProblemA 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/s2.

Slide 5-15

Example ProblemA 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/s2? 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