- Review energy and discuss how energy is conserved and changes forms - Investigate how energy works in pendulums and springs - Study the force of friction on a wooden block TODAY’S OUTCOMES: FORCE, MOTION AND ENERGY

Suppose a barge carrying 100,000 kg of coal (a bit more than 100 tons) is moving down the Ohio river at 10 m/sec when it is noticed that there is a fishing boat in the channel, 100 meters away. What force does the barge need to exert to stop before it hits the fishing boat? Solve this problem using 2 different methods: Method 1: Using the 3 Laws of Motion a) If the barge is to attain the speed of 0 m/sec when it reaches the boat, what will its average speed be? b) With this average speed, how much time will it take the barge to cover the distance between it and the boat? c) Given this time and the initial speed of 10 m/sec, what acceleration must the barge have to stop in time? d) Using the Law of Force and Acceleration, what force is required on the barge? speed = distance / time acceleration = change in speed / time = 10 m/sec / 20 sec = 0.5 m/sec 2 Force = mass × acceleration = 100,000 kg × 0.5 m/sec 2 = 50,000 Newtons Average speed = ½ × Initial speed = 5 m/sec time = distance / speed = 100 m / 5 m/sec = 20 sec

Method 2: Using the Conservation of Energy e) What is the kinetic energy of the moving barge? f) Using conservation of energy, what force is needed to stop the barge before it hits the boat? Kinetic energy = ½ mass × (velocity) 2 = 0.5 × 100,000 kg × (10 m/sec) 2 = 5,000,000 Joules Energy = Force × distance Force = Energy / distance = 5,000,000 Joules / 100 m = 50,000 Newtons Suppose a barge carrying 100,000 kg of coal (a bit more than 100 tons) is moving down the Ohio river at 10 m/sec when it is noticed that there is a fishing boat in the channel, 100 meters away. What force does the barge need to exert to stop before it hits the fishing boat?

- In this (and other examples), we saw the energy at the start was the energy at the finish. - Another way to state this is to say energy was conserved. You applied this principle in the last lab, when raising and dropping a metal ball. Changing direction of a cart 2 meters A kg (0.05 N) ball resting on the ground has zero energy.

You applied this principle in the last lab, when raising and dropping a metal ball. Changing direction of a cart 2 meters Raising the ball 2 meters gives the ball potential energy energy = force × distance = 0.05 N × 2 m = 0.1 Joules - In this (and other examples), we saw the energy at the start was the energy at the finish. - Another way to state this is to say energy was conserved.

You applied this principle in the last lab, when raising and dropping a metal ball. Changing direction of a cart 2 meters As the ball accelerates, the potential energy becomes kinetic energy Halfway down, the distance of the ball is half what it started, so it has only half its potential energy - the rest is now kinetic energy (½mv 2 ). - In this (and other examples), we saw the energy at the start was the energy at the finish. - Another way to state this is to say energy was conserved.

You applied this principle in the last lab, when raising and dropping a metal ball. Changing direction of a cart 2 meters At the bottom, the potential energy is again zero - it has all become kinetic energy. So, kinetic energy = ½mv 2 should be equal to the potential energy of 0.1 Joules. - In this (and other examples), we saw the energy at the start was the energy at the finish. - Another way to state this is to say energy was conserved.

You’ve heard since you were a young child in science class: ENERGY CANNOT BE CREATED OR DESTROYED. However - is energy always conserved within the system you are measuring? Changing direction of a cart This example assumes energy is conserved - is energy always conserved? (That is, can you create or destroy new energy?)

What happens AFTER the ball hits the ground? Does it still have stored energy or kinetic energy? Changing direction of a cart 2 meters Back to the falling ball example: The ball bounced a bit, so it had some kinetic energy left. What about when the ball comes to a complete rest? Where did the energy “go”? Some went into sound, some went into heat. Energy in the whole room is conserved, but things like friction can cause energy to leave the system you are measuring.

WHAT YOU ARE EXPECTED TO KNOW: - Potential energy is given by force × distance, and (in the absence of friction) does not depend on the path taken - Potential energy can be changed into kinetic energy - Solve problems involving force, mass and distance using kinetic and potential energy

A) is the correct answer. The moving freight car has a large kinetic energy. The man needs to take this energy away from the car. Energy = Force × distance, and since his force on the car is (relatively) small, he will need a long distance to stop the car. 19. A railway freight car is coasting on a level track with a small velocity (a few meters per second). A very strong man is trying to stop it by pulling on a rope. Which statement is correct? A) The man can stop the freight car, but he has to do so over a long distance. B) The man will not stop the car unless the force is larger than the weight of the freight car. C) The man will not stop the car unless the force is greater than the kinetic energy of the fright car. D) No matter how strong the man is, he will not be able to stop the freight car. 20. a) If a 5 kg goose flying south at 40 m/sec encounters a 1,000,000 kg jet plane flying north at 200 m/sec, how is the force of the goose on the jet plane related to the force of the jet plane on the goose? According to the Law of Interaction, the forces are equal and opposite! b) Suzanne observes that the goose gets smashed flat and the airplane hardly changes speed at all. Terry concludes from this that the force of the airplane on the goose must be much larger than the force of the goose on the airplane. Using considerations of energy, please reconcile Suzanne's observation with your answer to Q. 20 (that is explain how both you and Suzanne are right, whether you agree with Terry or not). Kinetic energy = ½ mass × (velocity) 2, so the more massive plane has MUCH more kinetic energy than the goose, so the plane is unharmed while the goose is squashed flat! Force on plane = – Force on goose MASS OF PLANE × acceleration of plane = – mass of goose × ACCELERATION OF GOOSE

22. a) A 1.5-Newton hockey puck slides 50 meters on ice. How much energy does it use? (Look back at the definition of energy before answering....) b) A goalie catches the puck in his glove, exerting a 50,000-Newton force over a distance of 2 cm. How much energy is absorbed by his glove? Energy = Force × distance, and the force must act along the direction of motion! 1.5 N is a weight pulling downward - there is no acceleration in the direction of motion (horizontal), so there is no energy used! Energy = Force × distance = 50,000 N × 0.02 m = 1000 J

23. So far, you have seen that, for all machines, energy in = energy out. Consider the example of a windlass (pictured right) composed of a crank handle and a rope wrapped around an axle. Here, the bucket weighs 30 Newtons, the radius of the axle is 10 cm (0.1 m) and the handle length is 40 cm (0.4 m). a) The circumference of a circle is 2 ✕ π ✕ radius. Find both the circumference of the axle, and the total distance your hand would move in one complete turn of the crank (that is, the circumference). b) Use your answer to a) to determine how far your hand would have to move to lift the bucket 1 meter. c) If energy in = energy out, what force is required to turn the crank handle to lift the 30-N bucket? Energy = Force × distance 1 meter of rope wraps around the axle - the handle has to turn once every time the axle turns once. Energy bucket = 30 N × 1 m = 30 J d axle = 2 × 3.14 × 0.1 m = 0.62 m d handle = 2 × 3.14 × 0.4 m = 2.51 m d handle / d axle = 2.51 / 0.62 = 4 The handle must be pushed 4 m for every 1 m of rope. Energy handle = ? × 4 m = 30 J ? = 7.5 N

- Review energy and discuss how energy is conserved and changes forms ✓ - Investigate how energy works in pendulums and springs - Study the force of friction on a wooden block TODAY’S OUTCOMES: FORCE, MOTION AND ENERGY