Physics. Chapter 7 Energy

Transcription

1 Physics Chapter 7 Energy

2 Work How long does a force act? Last week, we meant time as in impulse (Ft) This week, we will take how long to mean distance Force x distance (Fd) is what we call WORK W = Fd The heavier the load or the greater the distance, the more work is done.

3 Work F W = Fd d Fd = Newtons x meters 1 Newton Meter = 1 Joule

4 Power If we want to take into account how quickly the work was done, we re talking about POWER! The units for power are Watts 1 Watt = 1 Joule / second

5 Power Now calculate my power in lifting the water bottle.

6 Practice An object of mass 2 kg increases in speed from 2 m/s to 4 m/s in 3 s. What was the total work performed on the object during this time interval? An object weighing 40 newtons is dragged a distance of 20 meters by a force of 5 newtons in the direction of motion. What is the work done by the 5-newton force? How much work is done to lift a weight on 40 newtons to a height of 3 meters above the floor in 2 seconds? How much power does it take?

7 Mechanical Energy When work is done on an object, that object acquires energy. W = ΔE Energy is the ability to do work Energy comes in many forms for now, we will focus on Mechanical Energy

8 Mechanical Energy POTENTIAL ENERGY is energy stored and held in readiness by virtue of an object s position. A stretched rubber band A ball on top of a hill A compressed spring A drawn bow

9 Potential Energy

10 Potential Energy GRAVITATIONAL POTENTIAL ENERGY

11 Gravitational Potential Energy Gravitational PE = weight x height or PE = mgh Note that this is another form of our equation for work! W = Fd PE = (mg)h

12 Mechanical Energy KINETIC ENERGY is energy of motion. It is dependent on mass and velocity. A car driving down a highway A bullet fired from a gun Me walking my dog Anything in motion!

13 Kinetic Energy The equation for KE is not as straight forward as PE K = ½ m(δv) 2

14 Kinetic Energy

15 Kinetic Energy

16 Kinetic Energy

17 Potential & Kinetic Energy

18 Potential & Kinetic Energy

19 Potential & Kinetic Energy

20 Problems A rollercoaster car with mass m starts from rest at height h 1 on a frictionless rollercoaster. Derive an equation for the speed of the car when its height is h 2.

21 Problems Phil pushes Mala across the frictionless snow on her sled, starting from rest. He applies a force F for a distance d. How much work does Phil s applied force do? Derive an equation for the final speed of the sled.

22 Problems A toy car of mass m has a motor that can supply it with power P. Assume that the car begins at rest on a level floor and the motor is activated. Derive an equation for the speed of the car after a time t.

23 Potential & Kinetic Energy

24 Potential & Kinetic Energy

25 Potential & Kinetic Energy

26 Work Energy Theorem W = ΔKE

27 Work Energy Theorem

28 Conservation of Energy Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes.

29 Conservation of Energy

30 Conservation of Energy

31 Conservation of Energy

32 Practice A 40-newton object is lifted 10 meters above the ground and then released. After the object has fallen 4 meters and is 6 meters above the ground, what will its kinetic energy be? What will its kinetic energy be right before it hits the ground?

33 Practice A metal sphere M, whose mass is 2.0 kilograms, is suspended by a string from point P, as in a pendulum. The sphere is released from a vertical height h and passes through its lowest position (or rest position) with a speed of 10 meters per second. What is the approximate height from which the object was released?

34 Conservation of Energy

35 Newton s Cradle Would MOMENTUM be conserved in the situation below? v 2v (2m) (v)?=? (m) (2v) Yes! Momentum would be conserved!

36 Newton s Cradle Would ENERGY be conserved in the situation below? v 2v ( ½ ) (2m) (v) 2?=? ( ½ ) (m) (2v) 2 No way! Energy would NOT be conserved!

37 Check Questions 1. If a golf ball and a ping-pong ball both move with the same KE, can you say which has the greater speed? Explain. 2. In a gaseous mixture of heavy molecules and light molecules with the same average KE, can you say which have the greater speed? Explain. 3. Two lumps of clay with equal and opposite momenta have a head-on collision and come to rest. 1. Is momentum conserved? 2. Is KE conserved?

38 SAT Problems Note: On the SAT, you will see Kinetic Energy represented by K, and Potential Energy represented by U. Since energy is always conserved: K i + U i = K f + U f Let s look at problem 7.10 on Barron s Page 166

39 Work Done by a Spring Recall Hooke s Law, F s = kx The restoring force of a spring is therefore changing throughout the distance it acts, but is linear so we can use the average force when we are finding work done by a spring: F avg = ½ F s F avg = ½ k Δx

40 Work Done by a Spring Since W = Fd, work done on or by a spring is then: W s = F avg d parallel W s = (½ k Δx) (Δx) W s = (½ k Δx) (Δx) W s = Δ (½ kx 2 )

41 Practice A spring with a force constant k is stretched a distance x. By what factor must the spring s elongation be changed so that the elastic potential energy in the spring is doubled? A 4.0-kg mass is attached to a spring with a spring constant of 20 newtons per meter. The mass is lowered 0.50 meters to equilibrium, where it remains at rest. How much work was done stretching the spring?

42 Force Displacement Graphs The area under the graph of force against displacement is work. A variable force acts on a 5.0-kg mass, displacing the mass 10 meters as shown in the graph above. Determine the work done on the mass by the variable force.

43 Machines A machine is a device for multiplying force or changing the direction of a force. Every machine follows the conservation of energy. We will discuss two types of machines: Levers Pulleys

44 Levers A lever consists of a long board or pole and a fulcrum. Work Input = Work Output

45 Levers

46 Levera

47 Pulleys Pulleys are actually levers in disguise! In the arrangement below, only the direction of the force is changed. It is not multiplied.

48 Pulleys

49 Pulleys

50 Pulleys

51 Machines Machines are useful because they multiply force they give us Mechanical Advantage. Machines can multiply force at the expense of distance. Or they can multiply distance at the expense of force. BUT No machine can multiply (create) energy!!

52 Efficiency All the examples so far have been of Ideal Machines In reality, there s no such thing as an ideal machine Some energy is always lost in the transaction Usually converted to thermal energy