ESF 1124 Engineering Science

ESF 1124Fundamental PhysicsCHAPTER 5Energy, Work & PowerOutlineWork done by a constant forceWork done by variable force one dimensional caseKinetic energy and work-energy theoremPower & Conservation of EnergyGravitational Potential EnergyIntroductionThe concept of energy is one of the most important topics in science and engineering.Work is done by a force acting on an object when the point of application of that force moves through some distance and the force has a component along the line of motion.Define kinetic energy, which is energy an object possesses because of its motion.It is important to note that the work-energy concepts are based on Newtons laws and therefore allow us to make predictions that are always in agreement with these laws.Work Done by a Constant Force

Car is pushed along s displacement, but the amount of force F used to push it does not change.

Also known as Joule (J)A scalar quantitySI unit is Newton meter (Nm) Work is performed when an object undergoes a displacement d under the action of a constant force F.

For the diagram:

Assume that you push a car very, very, very hard until your veins pop out. But it did not move. Was any work done?

Exercise #1A man cleaning a floor pulls a vacuum cleaner with a force of magnitude F = 50.0 N at an angle of 30.0 with the horizontal.Calculate the work done by the force on the vacuum cleaner as the vacuum cleaner is displaced 3.00 m to the right.

Exercise #1 (solution)

Exercise #2 A particle moving in the xy plane undergoes a displacement d m as a constant force F N acts on the particle. Calculate the magnitude of the displacement d and that of the force, F.Calculate the work done by F.

Exercise #2 (solution)

Magnitude of the d and that of the force, F. Work done by F.Exercise #3 A person pushes 10 kg box at a constant velocity over a distance of 4 m. The coefficient of kinetic friction between the box and the floor is 0.3. How much work does the person do in pushing the box?Exercise #3 (solution) Since the box travels a constant velocity, the net force acting on the box is zero. That means that the force of the persons push is equal and opposite to the force of friction. The force of friction is give by RN, where is the coefficient of kinetic friction and RN is the reaction force. The reaction force is equal to the weight of the box, which is:

Exercise #4 A plank of length 5 m is inclined so that the higher end is 3 m above the lower. A block of mass 40 kg is dragged at constant speed up the plank against a friction force of 120 N. Find the total work done.Exercise #4 (solution) TW120 N 3 m5 mExercise #5

The weight lifter is bench-pressing a barbell whose weight is 710 N. In part (b) of the figure, he raises the barbell a distance of 0.65 m above his chest, and in part (c) he lowers it the same distance. The weight is raised and lowered at a constant velocity. Determine the work done on the barbell by the weight lifter during (a) the lifting phase and (b) the lowering phase.Exercise #5 (solution)

(a)

(b)

*(cos 1800 = -1)

A 120 kg crate on the flatbed of a truck that is moving with an acceleration of a = 1.5m/s2 along the positive x axis. The crate does not slip with respect to the truck, as the truck undergoes a displacement whose magnitude is s = 65m. What is the total work done on the crate by all of the forces acting on it?Exercise #6

Exercise #6 (solution) Forces that act on the crate: the weight W = mg of the crate, the normal force FN exerted by the flatbed, the static frictional force fs.

Work Done by Variable ForceA spring can be stretched out and in by varying force.Below shows a graph of a force acting on an object, say a ball, and the distance travelled.The force is constant at 5 N from point A to B. then from point B to C, the force starts to decline with time until it stop at rest.

Can you determine the amount of work done? From the force vs. displacement plot, work can be calculated as the area under the graph. 20 J5 JWhat if the varying force is not a straight line?From the force vs. displacement plot, work can be calculated as the area under the graph.

For a small displacement, x, W F x x

Over the total displacement:

Since work done is equal to the area under the curve:

The force acting on a particle is F(x)= (9x2 +3) N.Find the work done by the force on the particle as it moves it from x1 = 1.5m to x2 = 4m.Exercise #7 Exercise #7 (solution)

Kinetic Energy and Work-energy Theorem

It relates to things we do in everyday life, from fuel for transportation and heating, to electricity for lights and appliances, and foods for consumption.

Think of energy as the capacity that an object has for performing work.

Kinetic EnergyIt can be difficult to use Newtons second law to solve motion problems involving complex forces.An alternative approach is to relate the speed of a moving particle to its displacement under the influence of some net forceKinetic Energy (cont.)The formula that relates the energy on an object as a function of speed and mass is given as:

This formula represents the kinetic energy of an object.

Kinetic Energy (cont.)Kinetic energy is a scalar quantity and has the same units as work. For example, a 2.0-kg object moving with a speed of 4.0 m/s has a kinetic energy of 16 J.Work-Kinetic Energy TheoremWhen a moving object is acted on by another force, at which the object experiences a change in speed (work done), its kinetic energy changes. This change can be written as:

Where Ki is the initial kinetic energy and Kf is the final kinetic energy.

Work Done by a Spring

Fs = -kx (Spring force)Where;k = positive constant called force constant (measure of the stiffness of the spring, stiff springs have large k values, soft springs have small k values)x = the displacement of the block from its unstretched position

*The negative sign signifies that the force exerted by the spring is always directed opposite the displacement.

Work Done by a Spring

Power

PowerIt is interesting to know not only the work done by an object, but also the rate at which it is done.Compare for bottle of peanut butter and a 5 grams of explosives. Which of the two contain more energy?Power (cont.)The energy contained in both objects are very similar. The only difference is how fast the energy is released.Power (cont.)For simplicity sake, lets assume that both the bowl of cereal and the hand grenade is capable of releasing 1000 Joules of energy.The hand grenade releases all its energy in 1 second, while the bowl of cereal in 1 hour. How then do we differentiate the behaviour of these 2 items? We use the concept of power to differentiate them.Power (cont.)Average power is the rate at which energy is released/transferred can be written as:

What is the average power for the hand grenade and the bowl of cereal?In terms of power, hand grenade is a cereal killer.

Instantaneous PowerWe can define the instantaneous power P as the limiting value of the average power as t approaches zero:

Topic OutlineEfficiencyPotential energyConservative forceConservation of energyEfficiencyWe talked about the concept of energy previously, which is the capacity that an object has for doing work. It is now appropriate to introduce the term efficiency. Efficiency describes how well energy is utilized to perform a particular task. Efficiency (cont.)Take a car for example. Its engine is capable of converting energy contained inside the fuel (stored chemical energy) into mechanical energy, enabling the car to move. However, the conversion from chemical to mechanical energy isnt 100% efficient. Efficiency (cont.)Ideally we would like the following in a car:

Unfortunately we have this instead:Chemical Energy(fuel)Mechanical Energy(movement of car)Chemical Energy(fuel)HeatNoiseMechanical EnergyEfficiency (cont.)In this case, efficiency is ratio at which chemical energy is converted into mechanical energy, and it is written as:

Useful work here refers to energy in the form of mechanical energy which moves the car.Total work done refers to the energy released in the form of heat, noise and mechanical energy.

Gravitational Potential EnergyThere are several forms of potential energy: Elastic potential energy applicable to a block of springGravitational potential energyIn this chapter, we will focus specifically on gravitational potential energy.

Gravitational Potential Energy (cont.)As an object falls toward the Earth, the Earth exerts a gravitational force mg on the object, with the direction of the force being the same as the direction of the objects motion.It is extremely important to know that when gravitational force does work on the object and it increases the objects kinetic energy.Gravitational Potential Energy (cont.)Gravitational potential energy for an object with a distance (or height) h meters away from earth is given as:

Gravitational Potential Energy (cont.)When an object fall from height h2 to height h1, the change in potential energy is converted to kinetic energy.

h2h1Conservative ForceTo understand the concept of conservative force, lets look at 2 scenarios below:Ball initially at height h2Ball falls to height h1Conservative Force (cont.)What is its change in potential energy for both scenarios?

Ball initially at height h2Ball falls to height h1

Conservative Force (cont.)Notice that the change in potential energy for both scenario is independent of path taken?

Ball initially at height h2Ball falls to height h1Conservative Force (cont.)Now look at this scenario. What is the change in the potential energy of the ball as it moves from point A to B? Height h2ABConservative Force (cont.)We observe 2 things:Work done on the ball is independent of path takenThe work done on the ball moving through a closed path is zero. (A closed path is one in which the beginning and end points are identical.)

Conservative Force (cont.)Forces that exhibit such behaviour are termed conservative forces. In this case, the gravitational force is a conservative force.Conservation of EnergyEnergy can never be created or destroyed.It is merely transformed from one form to another, but the total energy of an isolated system is always constant.This is known as the conservation of energy.