Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Chapter 6 Work and Kinetic Energy

Copyright © 2012 Pearson Education Inc. Goals for Chapter 6 Understand & calculate work done by a force Understand meaning of kinetic energy Learn how work changes kinetic energy of a body & how to use this principle Relate work and kinetic energy when forces are not constant or body follows curved path To solve problems involving power

Copyright © 2012 Pearson Education Inc. Introduction The simple methods we’ve learned using Newton’s laws are inadequate when the forces are not constant. In this chapter, the introduction of the new concepts of work, energy, and the conservation of energy will allow us to deal with such problems.

Copyright © 2012 Pearson Education Inc. Work A force on a body does work if the body undergoes a displacement.

Copyright © 2012 Pearson Education Inc. Work done by a constant force The work done by a constant force acting at an angle  to the displacement is W = Fs cos .

Copyright © 2012 Pearson Education Inc. Work done by a constant force The work done by a constant force acting at an angle  to the displacement is W = Fs cos . Units of Work = Force x Distance = Newtons x meters - (Nm) = JOULE of energy!

Copyright © 2012 Pearson Education Inc. Positive, negative, and zero work A force can do positive, negative, or zero work depending on the angle between the force and the displacement.

Copyright © 2012 Pearson Education Inc. Positive, negative, and zero work A force can do positive, negative, or zero work depending on the angle between the force and the displacement.

Copyright © 2012 Pearson Education Inc. Positive, negative, and zero work A force can do positive, negative, or zero work depending on the angle between the force and the displacement.

Copyright © 2012 Pearson Education Inc. Positive, negative, and zero work A force can do positive, negative, or zero work depending on the angle between the force and the displacement. Work is done BY an external force, ON an object. Positive work done by an external force

Copyright © 2012 Pearson Education Inc. Positive, negative, and zero work A force can do positive, negative, or zero work depending on the angle between the force and the displacement. Work is done BY an external force, ON an object. Positive work done by an external force (with no other forces acting in that direction of motion)

Copyright © 2012 Pearson Education Inc. Positive, negative, and zero work A force can do positive, negative, or zero work depending on the angle between the force and the displacement. Work is done BY an external force, ON an object. Positive work done by an external force (with no other forces acting in that direction of motion) will speed up an object!

Copyright © 2012 Pearson Education Inc. Positive, negative, and zero work A force can do positive, negative, or zero work depending on the angle between the force and the displacement. Work is done BY an external force, ON an object. Positive work done by an external force (with no other forces acting in that direction of motion) will speed up an object! Negative work done by an external force ( wnofaitdom ) will slow down an object!

Copyright © 2012 Pearson Education Inc. Work done by several forces – Example 6.2 Tractor pulls wood 20 m over level ground; Weight = 14,700 N; Tractor exerts 5000 N force at 36.9 degrees above horizontal N friction opposes!

Copyright © 2012 Pearson Education Inc. Work done by several forces – Example 6.2 How much work is done BY the tractor ON the sled with wood? How much work is done BY gravity ON the sled? How much work is done BY friction ON the sled?

Copyright © 2012 Pearson Education Inc. Work done by several forces – Example 6.2 Tractor pulls wood 20 m over level ground; w = 14,700 N; Tractor exerts 5000 N force at 36.9 degrees above horizontal N friction opposes!

Copyright © 2012 Pearson Education Inc. Kinetic energy The kinetic energy of a particle is KE = 1/2 mv 2. Net work on body changes its speed & kinetic energy

Copyright © 2012 Pearson Education Inc. Kinetic energy The kinetic energy of a particle is K = 1/2 mv 2. Net work on body changes its speed & kinetic energy

Copyright © 2012 Pearson Education Inc. Kinetic energy The kinetic energy of a particle is K = 1/2 mv 2. Net work on body changes its speed & kinetic energy

Copyright © 2012 Pearson Education Inc. The work-energy theorem The work done by the net force on a particle equals the change in the particle’s kinetic energy. Mathematically, the work-energy theorem is expressed as W total = KE final – KE initial =  KE

Copyright © 2012 Pearson Education Inc. Work done by several forces – Example 6.3 Tractor pulls wood 20 m over level ground; w = 14,700 N; Tractor exerts 5000 N force at 36.9 degrees above horizontal N friction opposes! Suppose sled moves at 20 m/s; what is speed after 20 m?

Copyright © 2012 Pearson Education Inc. Using work and energy to calculate speed

Copyright © 2012 Pearson Education Inc. Forces on a hammerhead – example 6.4 Hammerhead of pile driver drives a beam into the ground. Find speed as it hits and average force on the beam.

Copyright © 2012 Pearson Education Inc. Forces on a hammerhead – example 6.4 Hammerhead of pile driver drives a beam into the ground, following guide rails that produce 60 N of frictional force

Copyright © 2012 Pearson Education Inc. Forces on a hammerhead – example 6.4 Hammerhead of pile driver drives a beam into the ground, following guide rails that produce 60 N of frictional force

Copyright © 2012 Pearson Education Inc. Comparing kinetic energies – example 6.5 Two iceboats have different masses, m & 2m. Wind exerts same force; both start from rest.

Copyright © 2012 Pearson Education Inc. Comparing kinetic energies – example 6.5 Two iceboats have different masses, m & 2m. Wind exerts same force; both start from rest. Which boat wins? Which boat crosses with the most KE?

Copyright © 2012 Pearson Education Inc. Work and energy with varying forces Many forces, such as force to stretch a spring, are not constant.

Copyright © 2012 Pearson Education Inc. Work and energy with varying forces—Figure 6.16 Many forces, such as force of a stretched spring, are not constant.

Copyright © 2012 Pearson Education Inc. Work and energy with varying forces—Figure 6.16 Approximate work by dividing total displacement into many small segments.

Copyright © 2012 Pearson Education Inc. Work and energy with varying forces—Figure 6.16 Work = ∫ F∙dx An infinite summation of tiny rectangles!

Copyright © 2012 Pearson Education Inc. Work and energy with varying forces—Figure 6.16 Work = ∫ F∙dx An infinite summation of tiny rectangles! Height: F(x) Width: dx Area: F(x)dx Total area: ∫ F∙dx

Copyright © 2012 Pearson Education Inc. Stretching a spring The force required to stretch a spring a distance x is proportional to x: F x = kx k is the force constant (or spring constant) Units of k = Newtons/meter –Large k = TIGHT spring –Small k = L O O S E spring

Copyright © 2012 Pearson Education Inc. Stretching a spring The force required to stretch a spring a distance x is proportional to x: F x = kx k is the force constant (or spring constant) of the spring. Area under graph represents work done on the spring to stretch it a distance X: W = ½ kX 2

Copyright © 2012 Pearson Education Inc. Work done on a spring scale – example 6.6 A woman of 600 N weight compresses spring 1.0 cm. What is k and total work done BY her ON the spring?

Copyright © 2012 Pearson Education Inc. Work done on a spring scale – example 6.6 A woman of 600 N weight compresses spring 1.0 cm. What is k and total work done?

Copyright © 2012 Pearson Education Inc. Motion with a varying force An air-track glider mass 0.1 kg is attached to a spring of force constant 20 N/m, so the force on the glider is varying. Moving at 1.50 m/s to right when spring is unstretched. Find maximum distance moved if no friction, and if friction was present with  k = 0.47

Copyright © 2012 Pearson Education Inc. Motion with a varying force glider mass 0.1 kg spring of force constant 20 N/m Moving at 1.50 m/s to right when spring is unstretched. Final velocity once spring stops glider = 0 We know 3 things! F/m = a; v i ; v f Why can’t we use F = ma ?

Copyright © 2012 Pearson Education Inc. Motion with a varying force An air-track glider is attached to a spring, so the force on the glider is varying. In general, if the force varies, using ENERGY will be an easier method than using forces! We know: Initial KE = ½ mv 2 Final KE = ½ mv f 2 = 0 Get net work done! Get ½ kx 2

Copyright © 2012 Pearson Education Inc. Motion with a varying force An air-track glider is attached to a spring, so the force on the glider is varying.

Copyright © 2012 Pearson Education Inc. Motion on a curved path—Example 6.8 A child on a swing moves along a smooth curved path at constant speed. Weight w, Chain length = R, max angle =  0 You push with force F that varies. What is work done by you? What is work done by gravity? What is work done by chain?

Copyright © 2012 Pearson Education Inc. Motion on a curved path—Example 6.8 A child on a swing moves along a curved path. Weight w, Chain length = R, max angle =  0 You push with force F that varies.

Copyright © 2012 Pearson Education Inc. Motion on a curved path—Example 6.8 W = ∫ F∙dl F∙dl = F cos  dl = ds (distance along the arc)

Copyright © 2012 Pearson Education Inc. Power Power is rate work is done. Average power is P av =  W/  t Instantaneous power is P = dW/dt. SI unit of power is watt (1 W = 1 J/s) horsepower (1 hp = 746 W ~ ¾ of kilowatt) kilowatt-hour (kwh) is ENERGY (power x time)

Copyright © 2012 Pearson Education Inc. Force and power In Example 6.9, jet engines develop power to fly the plane. Follow Example 6.9.

Copyright © 2012 Pearson Education Inc. A “power climb” A person runs up stairs. Refer to Figure 6.28 while following Example 6.10.