Newton s Laws - continued. Friction, Inclined Planes, N.T.L., Law of Gravitation

Transcription

1 ewton s Laws - continued riction, Inclined Planes,.T.L., Law of Gravitation

2 TWO types of riction Static riction that eeps an object at rest and prevents it from moving Kinetic riction that acts during motion

3 orce of riction The orce of riction is directly related to the orce ormal. Mostly due to the fact that BOTH are surface forces f sf f α µ constant of µ coefficient of µ s µ proportionality friction The coefficient of friction is a unitless constant that is specific to the material type and usually less than one. ote: riction OLY depends on the MATERIALS sliding against each other, OT on surface area.

4 Example A 500 crate is being pushed across a level floor at a constant speed by a force of 600 at an angle of 0 below the horizontal as shown in the figure. ay ax f a 0 mg f f a) What is the coefficient of inetic friction between the crate and the floor? µ + mg 600(sin 0) µ 705. ax ay µ 0.33 a cos 600(cos 0) a sin + 500

5 Example If the 600 force is instead pulling the bloc at an angle of 0 above the horizontal as shown in the figure, what will be the acceleration of the crate. Assume that the coefficient of friction is the same as found in (a) a 0 ax ay et ax a a ma f ma cos µ cos µ ( mg ma ma 600cos ( sin 0) a sin ) f 53.a mg a a m / s

6 Inclines f mg cos mg sin mg Tips Rotate Axis Brea weight into components Write equations of motion or equilibrium Solve

7 Example Masses m 4.00 g and m 9.00 g are connected by a light string that passes over a frictionless pulley. As shown in the diagram, m is held at rest on the floor and m rests on a fixed incline of angle 40 degrees. The masses are released from rest, and m slides.00 m down the incline in 4 seconds. Determine (a) The acceleration of each mass (b) The coefficient of inetic friction and (c) the tension in the string. m gcos40 T m f T m m g 40 ET ma T m g ma T ma + 40 m g sin ( f + T ) ma m g m g m gsin40

8 Example x v oxt + at 0 + a(4) a 0.5 m / s ET T ma m g ma T ma + mg g sin ( + T m a m f ) T 4 (.5) + 4(9.8) m m m m m µ g sin g sin g sin µ g sin µ m ( m a + m g) m a g cos m a m g g sin m a m g m a m f f T µ m g sin ma m g ma m g cos m a m a m g m a m a g cos µ

9 ewton s Third Law or every action there is an EQUAL and OPPOSITE reaction. This law focuses on action/reaction pairs (forces) They EVER cancel out All you do is SWITCH the wording! PERSO on WALL WALL on PERSO

10 .T.L This figure shows the force during a collision between a truc and a train. You can clearly see the forces are EQUAL and OPPOSITE. To help you understand the law better, loo at this situation from the point of view of ewton s Second Law. m Truc Truc A Truc Train M Train a Train There is a balance between the mass and acceleration. One object usually has a LARGE MASS and a SMALL ACCELERATIO, while the other has a SMALL MASS (comparatively) and a LARGE ACCELERATIO.

11 .T.L Examples Action: HAMMER HITS AIL Reaction: AIL HITS HAMMER Action: Earth pulls on YOU Reaction: YOU pull on the earth

12 ewton s Law of Gravitation What causes YOU to be pulled down? THE EARTH.or more specifically the EARTH S MASS. Anything that has MASS has a gravitational pull towards it. α Mm g What the proportionality above is saying is that for there to be a ORCE DUE TO GRAVITY on something there must be at least masses involved, where one is larger than the other.

13 .L.o.G. As you move AWAY from the earth, your DISTACE increases and your ORCE DUE TO GRAVITY decrease. This is a special IVERSE relationship called an Inverse- Square. g α r The r stands for SEPARATIO DISTACE and is the distance between the CETERS O MASS of the objects. We us the symbol r as it symbolizes the radius. Gravitation is closely related to circular motion as you will discover later.

14 .L.o.G Putting it all together mm g α r G constant of proportionality G Universal Gravitational Constant G 6.67x0 g m m G r 7 m g g g mg Use this when you are on the earth G m m r Use this when you are LEAVIG the earth

15 Try this! Let s set the equations equal to each other since they BOTH represent your weight or force due to gravity g g mg Use this when you are on the earth G m m r Use this when you are LEAVIG the earth Mm mg G r M g G r M Mass of the Earth r radius of the Earth 5.97x0 6.37x0 6 4 g m SOLVE OR g! 7 4 (6.67x0 )(5.97x0 ) g 9.8m / s 6 (6.37x0 )