Chapters 10 & 11: Energy

Transcription

1 Chapters 10 & 11: Energy

2 Power: Sources of Energy

3 Tidal Power SF Bay Tidal Power Project

4 Main Ideas (Encyclopedia of Physics) Energy is an abstract quantity that an object is said to possess. It is not something you can directly observe. The usefulness of the concept comes from the Conservation of Energy. In predicting the behavior of objects, one uses the Conservation of Energy to keep track of the total energy and the transfer of energy between its various forms and between objects. Work is the transfer of energy from one object to another by a force from one on the other that displaces the other. Power is the rate at which energy is transferred or, the rate at which work is done. Power is the FLOW of energy.

5 Conservation of Energy Energy can neither be created nor destroyed. It may change in form or be transferred from one system to another. The total amount of energy in the Universe is constant and can never change. E i E f Except for VERY brief amounts of time according to the Heisenberg Uncertainty Principle.

6 Ways to Transfer Energy Into or Out of A System Work transfers by applying a force and causing a displacement of the point of application of the force Mechanical Waves allow a disturbance to propagate through a medium Heat is driven by a temperature difference between two regions in space

7 More Ways to Transfer Energy Into or Out of A System Matter Transfer matter physically crosses the boundary of the system, carrying energy with it Electrical Transmission transfer is by electric current Electromagnetic Radiation energy is transferred by electromagnetic waves

8 Work Done by a Constant Force A force applied across a distance. W F r

9 Work-Energy Theorem The net work done changes the Kinetic Energy. If the velocity is constant, then the net work is zero. Wnet KE r 1 1 W KE F r ma r mv mv v v 2a r Notice: 2 2 net f i f i

10 Units Energy & Work are scalars and have units of the Joule: m 2 W Fd N m kg J s 2 1 m m 2 KE mv 2 kg( ) 2 kg J 2 s s 2

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12 Kinetic Energy The energy an object has due to its motion. KE 1 2 mv 2 IMPORTANT! v is the TOTAL velocity and is a scalar!!!

13 Kinetic Energy Table 7.1, p.194

14 Work Done by a Constant Force A force applied across a distance. W F r

15 If the Force and displacement are given by vectors use Scalar Product of Two Vectors! The scalar product of two vectors is written as A. B It is also called the dot product A B Ax Bx AyBy Az Bz A. B = A B cos q q is the angle between A and B q AB AB 1 cos ( ) W F r cosq Becomes W F r

16 Constant Force Problem If the resultant force acting on a 2.0-kg object is equal to (3i + 4j) N, what is the change in kinetic energy as the object moves from (7i 8j) m to (11i 5j) m? If the object was initially at rest, what is the final velocity? a. +36 J b. +28 J c. +32 J d. +24 J e. +60 J

17 Gravity and Air Resistance A 12-kg projectile is launched with an initial vertical speed of 20 m/s. It rises to a maximum height of 18 m above the launch point. How much work is done by the dissipative (air) resistive force on the projectile during this ascent? a kj b kj c kj d kj e kj

18 Work Done by a Varying Force The work done is equal to the area under the curve W x x i f F dx x where F x Fcosq

19 Varying Force Problem A force acting on an object moving along the x axis is given by Fx = (14x 3.0x 2 ) N where x is in m. How much work is done by this force as the object moves from x = 1 m to x = +2 m? a. +12 J b. +28 J c. +40 J d. +42 J e. 28 J

20 Work Done by a Varying Force Hooke s Law F s = - kx

21 Hooke s Law Ut tensio, sic vis - as the extension, so is the force Hooke s Law describes the elastic response to an applied force. Elasticity is the property of an object or material which causes it to be restored to its original shape after distortion. An elastic system displaced from equilibrium oscillates in a simple way about its equilibrium position with Simple Harmonic Motion.

22 Elastic Systems F kx Small Vibrations

23 Robert Hooke ( ) Leading figure in Scientific Revolution Contemporary and arch enemy of Newton Hooke s Law of elasticity Worked in Physics, Biology, Meteorology, Paleontology Devised compound microscope Coined the term cell

24 Hooke s Law F s = - kx The Restoring Force When x is positive (spring is stretched), F is negative When x is 0 (at the equilibrium position), F is 0 When x is negative (spring is compressed), F is positive

25 Hooke s Law It takes twice as much force to stretch a spring twice as far. The linear dependence of displacement upon stretching force: Fapplied kx

26 Hooke s Law Stress is directly proportional to strain. F ( stress) kx( strain) applied

27 Spring Constant k: Stiffness The larger k, the stiffer the spring Shorter springs are stiffer springs k strength is inversely proportional to the number of coils

28 Spring Question Each spring is identical with the same spring constant, k. Each box is displaced by the same amount and released. Which box, if either, experiences the greater net force?

29 Work Done by a Spring Identify the block as the system The work is the area under the Calculate the work as the block moves from x i = - x max to x f = 0 x f 0 1 Ws Fxdx x kx dx kx i xmax 2 The total work done as the block moves from x max to x max is zero. 2 max

30 Energy in a Spring What speed will a 25g ball be shot out of a toy gun if the spring (spring constant = 50.0N/m) is compressed 0.15m? Ignore friction and the mass of the spring. W Use Energy! spring KE ball 1 1 kx mv 2 2 v 2 2 k x m 50.0 N/ m v (.15 m) 6.7 m / s.025kg

31 Work done by a Spring The horizontal surface on which the block slides is frictionless. The speed of the block before it touches the spring is 6.0 m/s. How fast is the block moving at the instant the spring has been compressed 15 cm? k = 2.0 kn/m The mass of t he block is 2.0 kg. a. 3.7 m/s b. 4.4 m/s c. 4.9 m/s d. 5.4 m/s e. 14 m/s