Today: Work, Kinetic Energy, Potential Energy HW #4 due Thursday, 11:59 p.m. No Recitation Quiz this week

What is Energy ? Mechanical Electromagnetic PHY 211 PHY 213 Nuclear Chemical CHE 105 E = mc2 !!

Work in Physics By applying a force F, you have moved the car through a displacement Δx !! “That was a lot of work !!”

Work in Physics F x Δ x The work W done on an object by a constant force F during a linear displacement is given by: W = F Δx > 0 where F is the magnitude of the force, Δx is the magnitude of the displacement, and F and Δx point in the same direction. (scalar quantity) If F and Δx point in opposite directions, then W < 0 . SI Unit : Joule = N·m = kg·m2/s2

Work in Physics What if the force is NOT in the same direction as the displacement ? F y θ F cosθ x Δ x The work W done on an object by a constant force F during a linear displacement Δx is given (in general) by F = magnitude of force W = (F cos θ) Δx Δx = magnitude of displacement (scalar quantity) θ = angle between F and Δx

Sign (+ or –) of the Work Work can be either positive (> 0) or negative (< 0). F and Δx are magnitudes (so both > 0) W = (F cos θ) Δx cos θ determines the sign of W (+ or –) [ direction of F relative to Δx ] Lifting : upward force exerted by woman Work done by the woman is > 0. mg Δx Work done by gravity is < 0.

Sign (+ or –) of the Work Work can be either positive (> 0) or negative (< 0). F and Δx are magnitudes (so both > 0) W = (F cos θ) Δx cos θ determines the sign of W (+ or –) [ direction of F relative to Δx ] Lowering : upward force exerted by woman Work done by the woman is < 0. mg Δx Work done by gravity is > 0.

Work and Dissipative Forces Recall example worked in class of hockey puck sliding across ice : In this example, the work done by the force of kinetic friction is NEGATIVE (θ = 180°). Frictional work is (usually) negative. Negative work by friction results in the DISSIPATION of mechanical energy. The “lost energy” is primarily dissipated as HEAT.

Example A worker pushes a wheelbarrow 5.0 m along a level surface, exerting a constant horizontal force of 50.0 N. If a frictional force of 43 N acts on the wheelbarrow while it is moving, what is the NET WORK done on the wheelbarrow? 5.0 m 43 N 50 N

Example: 5.5 Starting from rest, a 5.0-kg block slides 2.50 m down a 30° ramp. The coefficient of kinetic friction between the block and ramp is μk = 0.436. Determine the : (a) Work done by the force of gravity. (b) Work done by the frictional force. (c) Work done by the normal force.

Kinetic Energy The kinetic energy of an object of mass m moving with a speed v is : SI unit : Joule = kg · m2/s2 (scalar quantity) Work-Energy Theorem : The net work done on an object is equal to the change in the object’s kinetic energy If Wnet > 0, the object’s speed increases If Wnet < 0, the object’s speed decreases

Kinetic Energy On previous slide, we thought of work as causing an increase or decrease in an object’s speed. Conversely, we can think of the kinetic energy as being equivalent to the amount of work a moving object can do in coming to rest.

Example: 5.15 A 7.8-gram bullet moving at 575 m/s penetrates a tree trunk to a depth of 5.50 cm. Use work and energy considerations to find the average frictional force that stops the bullet. Assuming the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving.

Example A 1000-kg car slams on the brakes, leaving 27.0-m long skid marks. Suppose a constant friction force of 8000 N acts on the car while it is skidding. What was the car’s minimum speed ?

Conservative vs. Non-Conservative Forces In general, there are two kinds of forces : “Conservative” Forces “Non-Conservative” Forces Energy can be recovered Energy cannot be recovered E.g., Gravity E.g., Friction Generally: Dissipative

Next Class 5.4 – 5.6 Spring Potential Energy, Energy Conservation, Power We will NOT cover 5.7