Part 2: Forces and the Laws of Motion

1. Part 2: Forces and the Laws of Motion Chapter 4

2. Part 2 • Newton’s Laws • Balanced vs. Unbalanced Forces • Drawing Free-Body Diagrams • Static Problems • Finding Net Forces on Inclined Planes • Two Body Problems

3. Objects in Equilibrium • Objects are at rest or have a constant velocity • Acceleration=0 • F=0 and Fx=0 and Fy=0

4. Free-Body Diagrams • Used to show relative magnitude and direction of all forces acting on an object • Size of arrow reflects magnitude of force • Direction of arrow shows direction of force • Label each arrow as to the type of force • Represent the object by a box Fn Fapp Fg

5. Finding Net External Forces Net force: vector sum of all forces (resultant) • Remember algebraic sum of vectors!! • Split x and y components for each vector. • Find Rx and Ry by adding each vectors components. • Use RxandRy to find resultant and angle. • Pay close attention to SIGNS!

6. Static Forces • When an object is at rest AND in a state of equilibrium (“static” means stationary or at rest) • Fnet=0 • Framing in buildings, signs hanging. • All materials have their breaking point or the tension (FT) that it can withstand.

7. Static Problems

8. Equal Angles • Fw is canceled out by the y-components of the FT • If the angles are EQUAL, Fy=Fw/2

9. Unequal Angles • If the angles are not equal, each x and y component needs to be analyzed and compared to one another. • Much more difficult!

10. Practice (pg. 94) • A traffic light weighing 100. N hangs from a vertical cable tied to two other cables that are fastened to a support. The upper cables make angles of 37.0° and 53.0° with the horizontal. Find the tension in each of the three cables.

11. Practice and Homework • Holt Physics Diagram Sheet as Guided Practice • Physics Static Problems Homework • Statics is critically important, we return to this topic when we study torque.

12. Inclined Planes • The greater the tilt of the surface, the faster the rate at which the object will slide. • Fn is perpendicular to the surface • Not opposite of weight anymore

13. Normal Force at an Angle • Find the x and y components of the weight vector Fparallel=Weight * sin  Fperpendicular=Weight * cos

14. Practice (pg. 95) A child holds a sled at rest on a frictionless, snow-covered hill (30.0° incline) . If the sled weighs 77.0 N, find the force exerted by the rope on the sled and the magnitude of the normal force exerted by the hill on the sled.

15. Practice (pg. 97) • A car of mass m is on an icy driveway inclined at an angle of 20.0°. Determine the acceleration of the car, assuming no friction. • If the length of the driveway is 25.0 m and the car starts from rest at the top, how long does it take to travel to the bottom? • What is the car’s speed at the bottom?

16. Review of Friction • Friction is proportional to Fn of an object • Friction depends on composition and quality and area of the surface coefficient of friction () • Static Friction Equations: Fs sFn • Kinetic Friction Equations: Fk=kFn

17. Practice 1 Without friction and a mass of 25 kg and an angle of 30.0°

18. Practice 2 • With frictionand a mass of 25 kg when the coefficient of friction between the mass and the 30.0° surface is 0.210.

19. Practice (pg. 102) Suppose a block with a mass of 2.50 kg is resting on a ramp. If the coefficient of static friction between the block and ramp is 0.350, what maximum angle can the ramp make with the horizontal before the block starts to slip down?

20. Practice and Homework • Friction Pre-lab Activity • Work in your lab groups, but if you do not finish, it will be individual homework. • This work can be used in tomorrow’s lab.

21. Friction Lab 2 Horizontal forces • Find weight of block plus 1.0 to 2.0kg Fg = • Find Normal force FN= • Pull with spring scale so that the block moves at a constant velocity. • This is FA= • Find frictional force and then find coefficient of kinetic friction. • Draw a free body diagram showing all forces, equation, and all work. Pull at an angle of 45 degrees (use protractor) block with an added 1kg mass on top. a. Find coefficient of kinetic friction. Draw a free body diagram as above. Did the value for coefficient change? • Should it? Why or why not? • Did the horizontal component of force change? • Why did the angled pull force increase? • Find % difference = Value 1- Value 2/ Avg of two values x 100%

22. Friction Lab 3 Find the coefficient of kinetic friction between the block (no added mass) and a large inclined plane at zero angle. Draw free body diagram all forces, all equations, and work. • DO NOT TEST ON INCLINED PLANE WHILE IT IS INCLINED AT ANGLE UNTIL YOU DO THE CALCULATIONS. Draw a free body diagram for an incline of 20 degrees with your block. Find the following: • Fg= Fgx= Fgy= FN= FFR= Calculate the minimum force required to pull this block up an incline of 20 degree at a constant velocity. Show work below. • NOW TEST THIS ON THE ACTUAL INCLINE PLANE! FIND % ERROR, SHOW WORK BELOW. Repeat these steps but now at an angle of 40 degrees. Show all forces on a free body diagram, all work. Test on the ramp and then find % error.

23. Two Body Problems • Involves 2 objects interacting by: • Contact with one another (Fcontact) • Connecting to one another with a string (Ftens) • Usually has 2 unknowns (F and a) • The forces between the two objects will be the same but in different directions • The acceleration will depend on the weights of the objects and applied force

24. Practice (pg. 105) A block of mass 5.00 kg rides on top of a second block of mass 10.0 kg. A person attaches a string to the bottom block and pulls the system horizontally across a frictionless surface. Friction between the two blocks keeps the 5.00 kg block from slipping off. If the coefficient of static friction is 0.350, what maximum force can be exerted by the string on the 10.0 kg block without causing the 5.00 kg block to slip?

25. Atwood Machine • Write an equation to find the acceleration of each mass.

26. Practice (pg. 104) A block with mass m1=4.00 kg and a ball with mass m2=7.00 kg are connected by a light string that passes over a frictionless pulley. The coefficient of kinetic friction between the block and the surface is 0.300. Find the acceleration of the two objects and the tension of the string.