{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Phys04

# Phys04 - Unit 4 Work and Energy 4.1 4.2 4.3 4.4 4.5 4.6...

This preview shows pages 1–4. Sign up to view the full content.

1 Unit 4 Work and Energy 4.1 Work and kinetic energy 4.2 Work - energy theorem 4.3 Potential energy 4.4 Total energy 4.5 Energy diagrams 4.6 A general study of the potential energy curve 4.1 Work and kinetic energy (1) Work: unit in joule (J) Work done by the force F d F = = = d F d F W x ) cos ( θ F x : the force along the displacement Remark: Positive work is done on an object when the point of application of the force moves in the direction of the force. Mathematical statement: Work done is the dot product of the force and the displacement. Dot product: AB ⋅= = + + AB A B A B A B xx yy zz cos Example A 75.0-kg person slides a distance of 5.00m on a straight water slide, dropping through a vertical height of 2.50 m. How much work does gravity do on the person? y x F G F G d G d =5.00 m h= 2.5 mg

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Answer: The gravity along the displacement has a magnitude mg cos θ . By the definition of work done, the work done of the gravity on the person is given by W = ( mg cos ) d = mg ( h / d ) d = mgh = (75.0)(9.8)(2.50) = 1837.5 J Remark: When F or d is not a constant (see the left figure, the movement of the particle is always varying). i i w s F i = W ii i =⋅ Fs where s i is extremely small. The work done of the gravity on the ball’s falling down is given by mgh y mg y F y x F - d W h h C C = = = + = = 0 0 d d ) ˆ d ˆ d ( ˆ j i j s F (2) Power: work done per unit time Power == = lim t W t dW dt d dt 0 Since dt d s v = , we have the power equals to the dot product of force and velocity. e.g. Power v F = If the force and the velocity are in the same direction, P = Fv. (3) Kinetic energy 2 2 1 mv K 4.2 Work - energy theorem If an object is moving with an acceleration a and a distance d is moved, then according to the formula ad v v i f 2 2 2 + = , we have d m F v v i f ) ( 2 2 2 + = . The work done on the object W is given by i f i f i f K K mv mv v v m Fd W = = = = 2 2 2 2 2 1 2 1 ) ( 2 Or, we can rewrite it as fi WK K K =− = . y x mg h C ( h , h ) (0, 0) F G F G d G v i v f
3 The work-energy theorem states that the total work done on the object by the forces equals the change in kinetic energy. Remark: A proof by using integration. Suppose a particle moves in a straight line (1-D) WF x d x x x i f = () Fm am dv dt == , v dx dt = ∴= = = ∫∫ Wm dv dt dx mdv dx dt mvdv x x x x v v i f i f i f () =−= 1 2 2 1 2 2 mv mv K K fi f i 4.3 Potential energy The gravitational potential energy U = mgh The difference of the potential energy: U = U f U i = W , where W is the work done by gravity if the block is released. In this case, W is positive. When a spring is compressed by an amount x , the work done of the applied force 2 0 0 2 1 kx kxdx Fdx x x = = = ( F : applied force) Uk x = 1 2 2 potential energy of a spring.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 11

Phys04 - Unit 4 Work and Energy 4.1 4.2 4.3 4.4 4.5 4.6...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online