- Review oscillations and friction - Study several demonstrations that review the concepts of force, motion and energy TODAY’S OUTCOMES: FORCE, MOTION AND ENERGY

When the car accelerates forward, the inertia of the map tends to keep it still, unless the force of friction is strong enough to accelerate it at the same rate as the car. If the car accelerates too quickly, the friction force isn’t strong enough to pull the map forward with the car. 1. When Miriam and Harold go on trips, they put the map on the passenger-side dashboard, in case they need to look at it. On their way out of town, the map falls off the dashboard at every stoplight, just after the light turns green.. (A) Why does the map fall off the dashboard at the stoplights? Discuss the role played by any of the laws of motion that are relevant. (B) Harold says that the maps wouldn’t fall off if Miriam would change her driving style. What change is he recommending? If Miriam would lower the acceleration of the car (by letting up on the gas a bit), the force of friction of the dashboard on the map would be strong enough to match the acceleration of the car, and the map would stay put.

FORCES ON A BLOCK PULLED ACROSS A TABLE AT CONSTANT SPEED Friction Force of table on block Pull on the string Weight

Friction FORCES ON A BLOCK PULLED ACROSS A TABLE AT CONSTANT SPEED Force of table on block Pull on the string Weight WEIGHT INCREASES ⇒ FORCE OF TABLE INCREASES ⇒ FRICTION INCREASES ⇒ FORCE NEEDED TO PULL THE BLOCK INCREASES IF SPEED IS CONSTANT, THESE FORCES ARE BALANCED

FRICTION CAUSES ENERGY TO LEAVE YOUR SYSTEM Energy is conserved, but it can change from measured potential and kinetic energy into heat and sound. Potential energy = Weight × height Kinetic energy = 0 Rolling ball - not much friction Potential energy = 0 Kinetic energy = ½mv 2 = weight × initial height Potential energy = Weight × height Kinetic energy = 0 Sliding box - lots of friction Potential energy = 0 Kinetic energy = ½mv 2 < weight × initial height energy lost to heat

OSCILLATIONS Oscillations can be looked at in terms of force and acceleration, or in terms of energy.

OSCILLATIONS Pendulum: Force and Acceleration tension weight weight and tension are NOT equal and opposite here, so there is a net force, and thus an ACCELERATION net force

OSCILLATIONS Pendulum: Force and Acceleration tension weight At the bottom, tension and weight cancel - no net force

OSCILLATIONS Pendulum: Force and Acceleration on the swing upward, forces become unbalanced again, net force reappears tension weight net force Acceleration in a pendulum is always toward the central line, or equilibrium position (where it would hang if stationary.)

OSCILLATIONS Pendulum: Energy Potential energy is stored as pendulum is pulled back; there is no motion or kinetic energy yet

OSCILLATIONS Pendulum: Energy At the bottom, the potential energy is gone - but speed and kinetic energy are highest

OSCILLATIONS Pendulum: Energy on the swing upward, the speed and kinetic energy lower; potential energy is again stored

OSCILLATIONS SPRING: Force and acceleration “restoring” force pull from hand When the spring is “pulled back”, the pull from your hand and the restoring force are balanced equilibrium line

OSCILLATIONS SPRING: Force and acceleration “restoring” force When you release, you remove the force from your hand - forces are no longer balanced - restoring force = the net force net force SPRING ACCELERATES UP

OSCILLATIONS SPRING: Force and acceleration When the spring returns to equilibrium position, it is MOVING quickly, but there is no more restoring force; NO ACCELERATION at this instant no net force

OSCILLATIONS SPRING: Force and acceleration “restoring” force When the spring passes the equilibrium line, the restoring force pulls the other way net force SPRING ACCELERATES DOWN

OSCILLATIONS SPRING: Energy When the spring is pulled down, POTENTIAL ENERGY is stored in the spring

OSCILLATIONS SPRING: Energy As the spring passes the equilibrium, there is no more potential energy; but the speed is maximum, along with kinetic energy

OSCILLATIONS SPRING: Energy As the spring reaches the other side, it slows, and kinetic energy again becomes potential energy

MASS OF SPRING vs. PENDULUM SPRING Mass increases, restoring force stays same; so acceleration decreases Frequency decreases with mass PENDULUM Mass increases, restoring force (weight) also increases, so acceleration stays the same Frequency does not depend on mass

- Friction can cause energy to decrease in a measured system. - Energy changes back and forth between kinetic energy and potential energy in an oscillating system - Increasing mass affects the period of a spring, but not a pendulum WHAT YOU ARE EXPECTED TO KNOW:

INSTRUCTIONS FOR TODAY: 1) Find the station assigned to your group number in your packet. You will do this activity first, answer questions, and present the results at the end of class. You will be given 10 minutes to run through the first activity. 2) You will then rotate around the room to try out (and complete as much as possible) the other stations in the room - we will announce a “switch” every 5 minutes. 3) When all 11 stations are complete, return to your table and discuss how to summarize your results in class discussion. 4) We will then rotate the discussion from group to group as a review.

- Review oscillations and friction ✓ - Study several demonstrations that review the concepts of force, motion and energy TODAY’S OUTCOMES: FORCE, MOTION AND ENERGY

B) Use the Laws of Motion to find the acceleration of the penny. Use the acceleration to find how much time it takes for the penny to stop; from there you can (and should) find the distance the penny moves. A) This example is an exact analogy to the slowing barge problem you worked on a couple classes ago, except in this case you are given the force, and have to solve for the distance. label the analogous quantities in these 2 problems. Use a “?” for an unknown variable. For example (do the rest yourself!): mass of barge (100,000 kg) ↔ mass of penny (0.004 kg) initial speed of barge (10 m/sec) ↔ initial speed of penny (0.5 m/sec) A game you can play is to give a penny a shove so that it slides across a table, trying to get it to stop on a target. You wish to find out how far the penny will go before it stops, if you give it a certain initial speed. Assume you give the penny an initial speed of 0.5 m/sec, and that the force of friction from the table is about N. A penny has a mass of about 4 g = kg. Force = mass × acceleration ⇒ acceleration = Force/mass force on barge (?) ↔ force of friction on penny (0.002 N) distance in which barge stops (100 m) ↔ distance in which penny stops (?) final speed of barge (0 m/sec) ↔ final speed of penny (0 m/sec) acceleration = change in velocity/time ⇒ time = change in velocity/acceleration average speed = distance/time ⇒ distance = average speed × time (Remember average speed = ½ × initial speed)