Class 20: Work and kinetic energy Test 2 1. Next Wednesday (March 4) - - PowerPoint PPT Presentation

Class 20: Work and kinetic energy

Test 2

• 1. Next Wednesday (March 4) 11:00‐11:50 in this class

room.

• 2. Newton’s Law of gravitation, Hooke’s Law, Newton’s Law
• f motion.
• 3. No formula or cheat sheet.
• 4. 8 multiple choice problems (5 points each) and 2 long (30

points each) problems. Total 100 points.

• 5. Calculators allowed, but not the program function (though

I don’t think it will help).

• 6. Please bring photo ID.
• 7. No reschedule of test even though you have more than

two tests that day.

• 8. Classwork Monday will be 8 multiple choices on the test

materials.

Problem solved? Problem is solve if we know F as a function of time. If we can solve the differential equations, we will know the position and velocity of the particle at any time.

z dt d m F y dt d m F x dt d m F

2 2 z 2 2 y 2 2 x

     

The problem In most cases we live in a “force field” – there is always a force acting on us and this force depends on where we are.

x

z dt d m F y dt d m F x dt d m F

2 2 z 2 2 y 2 2 x

     

Acceleration by chain rule (1D)

If we know the velocity as a function of time, we can differentiate it w.r.t. time and find out how the acceleration depends on time:

dt dv a

x 

However, very often we only know the velocity as a function of position (i.e. coordinate x). What to do in this case?

dx dv v a dx dv dt dx dt dv a

x x

   

The answer

In most cases we live in a “force field” – there is always a force acting on us and this force depends on where we are.

x

dx F mv 2 1

• mv

2 1 F v dx d v m v dx d m F x dt d m F

x x x 2 xi 2 xf x x x x x 2 2 x

f i



              

3D

dz F mv 2 1

• mv

2 1 dy F mv 2 1

• mv

2 1 dx F mv 2 1

• mv

2 1

z z z 2 iz 2 fz y y y 2 iy 2 fy x x x 2 ix 2 fx

f i f i f i

  

                    

+

                

  

dz F dy F dx F mv 2 1

• mv

2 1

z z z y y y x x x 2 i 2 f

f i f i f i

Work (abbreviation: W)

dz F dy F dx F F

z z z y y y x x x

f i f i f i

  

   

Work done W by a force

• 1. Work is a scalar (sum of definite integrals) – it has no

direction.

• 2. Unit of work: Joule (J). Joule is not a fundamental

unit, J  Nm  Kgm2s‐2.

• 3. Work done by a force can be positive, negative, or 0.