Ying Yi PhD Chapter 6 Work and Energy 1 PHYS HCC

Forms of Energy Mechanical Focus for now May be kinetic (associated with motion) or potential (associated with position) Chemical Electromagnetic Nuclear 2 PHYS HCC

Outline PHYS HCC 3 Work Work-Energy Theorem Potential Energy  Gravitational Potential Energy Power

Work (Link between force and energy) Definition: The work, W, done by a constant force on an object is defined as the product of the component of the force along the direction of displacement and the magnitude of the displacement Units: Newton meter = Joule N m = J J = kg m 2 / s 2 4 PHYS HCC

5 Work (Same direction) W = F  x This equation applies when the force is in the same direction as the displacement are in the same direction

PHYS HCC 6 Work (Different Direction) W = (F cos  )  x F is the magnitude of the force Δ x is the magnitude of the object’s displacement q is the angle between Question: Does work have anything to do with velocity and acceleration? Is work a scalar or vector?

Work (Multiple forces) If there are multiple forces acting on an object, the total work done is the algebraic sum of the amount of work done by each force 7 PHYS HCC

False or True Questions PHYS HCC 8 When the force is perpendicular to the displacement cos 90° = 0, the work done by a force is zero. Work can be positive and negative. True

PHYS HCC 9 Work Can Be Positive or Negative Work is positive when lifting the box Work would be negative if lowering the box The force would still be upward, but the displacement would be downward

Example 6.1 Pulling a suitcase PHYS HCC 10 Find the work done by a 45.0 N force in pulling the suitcase in Figure 6.2a at an angle Ɵ =50.0º for a distance s=75.0 m.

Group Problem: Sledding PHYS HCC 11 An Eskimo returning from a successful fishing trip pulls a sled loaded with salmon. The total mass of the sled and salmon is 50.0 kg, and the Eskimo exerts a force of magnitude 1.20×10 2 N on the sled by pulling on the rope. (a) How much work does he do on the sled if Ɵ =30.0° and he pulls the sled 5.00 m? (Treat the sled as a point particle, so details such as the point of attachment of the rope make no difference.) (b) At a coordinate position of 12.4 m, the Eskimo lets up on the applied force. A friction force of 45.0 N between the ice and the sled brings the sled to rest at a coordinate position of 18.2 m. How much work does friction do on the sled?

Work & Kinetic Energy PHYS HCC 12 Recall motion equation: Work Energy Theory

Kinetic Energy Energy associated with the motion of an object Scalar quantity with the same units as work Work is related to kinetic energy 13 PHYS HCC

Work-Kinetic Energy Theorem When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy Speed will increase if work is positive Speed will decrease if work is negative 14 PHYS HCC

Example 6.5: Skiing PHYS HCC 15 A 58 kg skier is coasting down a 25º slope, as Figure 6.7a shows. Near the top of the slope, her speed is 3.6 m/s. she accelerates down the slope because of the gravitational force, even though a kinetic frictional force of magnitude 71 N opposes her motion. Ignoring air resistance, determine the speed at a point that is displaced 57 m downhill.

Group Problem: Ion propulsion Drive PHYS HCC 16 The space probe Deep Space I was launched October 24, 1998, and it used a type of engine called an ion propulsion drive. An ion propulsion drive generates only a weak force (or thrust), but can do so for long periods of time using only small amounts of fuel. Suppose the probe, which has a mass of 474 kg, is traveling at an initial speed of 275 m/s. No forces act on it except the 5.60×10 -2 N thrust of its engine. This external force F is directed parallel to the displacement s, which has a magnitude of 2.42 ×10 9 m. Determine the final speed of the probe, assuming that its mass remains nearly constant.

Types of Forces There are two general kinds of forces Conservative Work and energy associated with the force can be recovered Nonconservative The forces are generally dissipative and work done against it cannot easily be recovered 17 PHYS HCC

Conservative Forces A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points Examples of conservative forces include: Gravity Spring force Electromagnetic forces 18 PHYS HCC

Nonconservative Forces A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points. Examples of nonconservative forces Kinetic friction, air drag, propulsive forces 19 PHYS HCC

20 Nonconservative Force (Friction) The blue path is shorter than the red path The work required is less on the blue path than on the red path Friction depends on the path and so is a non-conservative force

Work done by conservative force PHYS HCC 21 Gravitational potential energy

Potential Energy Potential energy is associated with the position of the object within some system Potential energy is a property of the system, not the object A system is a collection of objects interacting via forces or processes that are internal to the system 22 PHYS HCC

Work and Potential Energy For every conservative force a potential energy function can be found Evaluating the difference of the function at any two points in an object’s path gives the negative of the work done by the force between those two points 23 PHYS HCC

Gravitational Potential Energy Gravitational Potential Energy is the energy associated with the relative position of an object in space near the Earth’s surface Objects interact with the earth through the gravitational force Actually the potential energy is for the earth-object system 24 PHYS HCC

25 Work and Gravitational Potential Energy PE = mgy Units of Potential Energy are the same as those of Work and Kinetic Energy

Reference Levels for Gravitational Potential Energy Often the Earth’s surface May be some other point suggested by the problem Once the position is chosen, it must remain fixed for the entire problem 26 PHYS HCC

27 Reference Levels, cont At location A, the desk may be the convenient reference level At location B, the floor could be used At location C, the ground would be the most logical reference level The choice is arbitrary, though

Example: Skis PHYS HCC 28 A 60.0 kg skier is at the top of a slope, as shown in Figure 5.14, At the initial point A, she is 10.0 m vertically above point B. (a) Setting the zero level for gravitational potential energy at B, find the gravitational potential energy of this system when the skier is at A and then at B. Finally, find the change in potential energy of the skier-Earth system at the skier goes from point A to point B. (b) Repeat this problem with the zero level at point A. (c) Repeat again, with the zero level 2.00 m higher than point B.

Work-Energy Theorem, Extended The work-energy theorem can be extended to include potential energy: If other conservative forces are present, potential energy functions can be developed for them and their change in that potential energy added to the right side of the equation 29 PHYS HCC

Conservation of Energy Total mechanical energy is the sum of the kinetic and potential energies in the system Other types of potential energy functions can be added to modify this equation 30 PHYS HCC

Problem Solving with Conservation of Energy Define the system Verify that only conservative forces are present Select the location of zero gravitational potential energy, where y = 0 Do not change this location while solving the problem Identify two points the object of interest moves between One point should be where information is given The other point should be where you want to find out something 31 PHYS HCC

Problem Solving, cont Apply the conservation of energy equation to the system Immediately substitute zero values, then do the algebra before substituting the other values Solve for the unknown Typically a speed or a position Substitute known values Calculate result 32 PHYS HCC

Example 6.8 Motorcyclist PHYS HCC 33 A motorcyclist is trying to leap across the canyon by driving horizontally off the cliff at a speed of 38.0 m/s. Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side.

Work-Energy With Nonconservative Forces If nonconservative forces are present, then the full Work-Energy Theorem must be used instead of the equation for Conservation of Energy Often techniques from previous chapters will need to be employed 34 PHYS HCC

Group Problem PHYS HCC 35 Waterslides are nearly frictionless, hence can provide bored students with high-speed thrills (Fig. 5.18). One such slide, Der Stuka, named for the terrifying German dive bombers of World War II, is 72.0 feet high (21.9 m), found at Six Flags in Dallas, Texas. (a) Determine the speed of a 60.0 kg woman at the bottom of such a slide, assuming no friction is present. (b) If the woman is clocked at 18.0 m/s at the bottom of the slide, find the work done on the woman by friction.

Nonconservative Forces with Energy Considerations When nonconservative forces are present, the total mechanical energy of the system is not constant The work done by all nonconservative forces acting on parts of a system equals the change in the mechanical energy of the system 36 PHYS HCC

Nonconservative Forces and Energy In equation form: The energy can either cross a boundary or the energy is transformed into a form of non- mechanical energy such as thermal energy 37 PHYS HCC

Transferring Energy By Work By applying a force Produces a displacement of the system Heat The process of transferring heat by collisions between atoms or molecules For example, when a spoon rests in a cup of coffee, the spoon becomes hot because some of the KE of the molecules in the coffee is transferred to the molecules of the spoon as internal energy 38 PHYS HCC

Transferring Energy Mechanical Waves A disturbance propagates through a medium Examples include sound, water, seismic Electrical transmission Transfer by means of electrical current This is how energy enters any electrical device 39 PHYS HCC

Transferring Energy Electromagnetic radiation Any form of electromagnetic waves Light, microwaves, radio waves For example Cooking something in your microwave oven Light energy traveling from the Sun to the Earth 40 PHYS HCC

Notes About Conservation of Energy We can neither create nor destroy energy Another way of saying energy is conserved If the total energy of the system does not remain constant, the energy must have crossed the boundary by some mechanism Applies to areas other than physics 41 PHYS HCC

Power Often also interested in the rate at which the energy transfer takes place Power is defined as this rate of energy transfer SI units are Watts (W) 42 PHYS HCC

Power, cont. US Customary units are generally hp Need a conversion factor Can define units of work or energy in terms of units of power: kilowatt hours (kWh) are often used in electric bills This is a unit of energy, not power 43 PHYS HCC

Example 6.13 The power to Accelerate a car PHYS HCC 44 A car, starting from rest, accelerates in the +x direction. It has a mass of 1.10 × 10 3 kg and maintains an acceleration of m/s 2 for 5.00 s. Assume that a single horizontal force accelerates the vehicle. Determine the average power generated by this force.

Homework PHYS HCC 45 3, 5, 10, 14, 15, 21, 24, 32, 40, 43, 46, 65