Dr. Derrick Boucher Assoc. Prof. of Physics PHY 2048C General Physics I with lab Spring 2011 CRNs 11154, 11161 & 11165 Dr. Derrick Boucher Assoc. Prof. of Physics Sessions 11-12, Chapter 10

Chapter 9 Homework Due Friday 2/18 @ midnight Chapter 10 Homework Due Tuesday 2/22 @ midnight

Chapter 10 Practice Problems 5, 7, 29, 31, 33, 35, 47, 53 Unless otherwise indicated, all practice material is from the “Exercises and Problems” section at the end of the chapter. (Not “Questions.”)

Money-Energy Analogy From the Parable of the Lost Penny

Money—Energy Analogy From the law of conservation of energy

Kinetic and Potential Energy There are two basic forms of energy. Kinetic energy is an energy of motion Gravitational potential energy is an energy of position The sum K + Ug is not changed when an object is in freefall. Its initial and final values are equal

Energy Units SI: joule (J) Other popular units: calorie, Calorie, BTU (British Thermal Unit), foot-pound, erg, electron-volt, kilowatt-hour (kWh), therm, Hartree, Rydberg…

Kinetic and Potential Energy IMPORTANT: The potential energy ONLY depends on the height, even if the object moves along a ramp, hill, etc.

The Zero of Potential Energy You can place the origin of your coordinate system, and    thus the “zero of potential energy,” wherever you choose    and be assured of getting the correct answer to a problem. The reason is that only ΔU has physical significance, not   Ug itself.

The Zero of Potential Energy

The Zero of Potential Energy

Conservation of Mechanical Energy The sum of the kinetic energy and the potential energy of a system is called the mechanical energy. Here, K is the total kinetic energy of all the particles in the system and U is the potential energy stored in the system. The kinetic energy and the potential energy can change, as they are transformed back and forth into each other, but their sum remains constant.

Problem-Solving Strategy: Conservation of Mechanical Energy

Problem-Solving Strategy: Conservation of Mechanical Energy

Example, Problem 10-13, p. 296

Chapter 10. Clicker Questions

half as much kinetic energy as the first. twice as much kinetic energy as the first. Four times as much kinetic energy as the first. Answer: C © 1997 Lewis Carroll Epstein

half as much kinetic energy as the first. twice as much kinetic energy as the first. four times as much kinetic energy as the first. Answer: C © 1997 Lewis Carroll Epstein

The lawyer’s question cannot be answered from the given information Preparing his case for trial, a lawyer pondered this question. A 1-N flowerpot fell one meter from a shelf and struck his client squarely on the head. How much force did the pot exert on his client’s head? 1 N 4.9 N 9.8 N 19.6 N The lawyer’s question cannot be answered from the given information Answer: C © 1997 Lewis Carroll Epstein

Hooke’s Law If you stretch a rubber band, a force appears that tries to pull the rubber band back to its equilibrium, or unstretched, length. A force that restores a system to an equilibrium position is called a restoring force. If s is the position of the end of a spring, and se is the equilibrium position, we define Δs = s – se. If (Fsp)s is the s-component of the restoring force, and k is the spring constant of the spring, then Hooke’s Law states that The minus sign is the mathematical indication of a restoring force.

Hooke’s Law

Example, Problem 10-16, p. 296

Elastic Potential Energy Consider a before-and-after situation in which a spring launches a ball. The compressed spring has “stored energy,” which is then transferred to the kinetic energy of the ball. We define the elastic potential energy Us of a spring to be

Example, Problem 10-45, p. 298

Chapter 9. Quiz Get your clickers ready

Impulse is a force that is applied at a random time. a force that is applied very suddenly. the area under the force curve in a  force-versus-time graph. the time interval that a force lasts. Answer: C

The total momentum of a system is conserved always. if the system is isolated. if the forces are conservative. never; it’s just an approximation. Answer: B

In an inelastic collision, impulse is conserved. momentum is conserved. force is conserved. energy is conserved. elasticity is conserved. Answer: B

A 0.24 kg blob of clay is thrown at a wall with an initial velocity of 23 m/s. If the clay comes to a stop in 91 ms, what is the average force experienced by the clay? A) 0.5 N B) 2.1 N C) 61 N D) 122 N

A 1200 kg ore cart is rolling at 10. 8 m/s across a flat surface A 1200 kg ore cart is rolling at 10.8 m/s across a flat surface. A crane dumps 691 kg of ore (vertically) into the cart. How fast does the cart move after being loaded with ore? Assume that frictional forces may be neglected. A) 6.2 m/s B) 4.1 m/s C) 10.8 m/s D) 6.8 m/s

Elastic Collisions

Elastic Collisions Consider a head-on, perfectly elastic collision of a ball of mass m1 having initial velocity (vix)1, with a ball of mass m2 that is initially at rest. The balls’ velocities after the collision are (vfx)1 and (vfx)2.These are velocities, not speeds, and have signs. Ball 1, in particular, might bounce backward and have a negative value for (vfx)1.

Elastic Collisions Consider a head-on, perfectly elastic collision of a ball of mass m1 having initial velocity (vix)1, with a ball of mass m2 that is initially at rest. The solution, worked out in the text, is

The Equations for Elastic collisions These do not appear on the equation sheet but should be used for homework. I will provide these separately for the next exam (on the board).

Example, Problem 10-28, p. 297

Energy Diagrams A graph showing a system’s potential energy and total energy as a function of position is called an energy diagram.

Energy Diagrams The kinetic energy is the difference between the total energy (TE) and the potential energy (PE).

Energy diagrams are commonly used in chemistry. E. g Energy diagrams are commonly used in chemistry. E.g. molecular vibrations. The different vibrational energy levels (v= 0,1,2…) are different average kinetic energy levels of the molecule. Most molecular bonds are approximately “springs” for the lowest vibrational energy levels.

Another chemistry example

Example, Problem 10-32, p. 297

Chapter 10. Clicker Questions

more momentum into the ground. less momentum into the ground. A runner starts from rest. She puts a certain amount of momentum into herself and more momentum into the ground. less momentum into the ground. the same amount of momentum into the ground. Answer: C © 1997 Lewis Carroll Epstein

more kinetic energy into the ground. A runner starts from rest. She puts a certain amount of kinetic energy into herself and more kinetic energy into the ground. less kinetic energy into the ground. the same amount of kinetic energy into the ground. Answer: B © 1997 Lewis Carroll Epstein