Lecture 8: Forces & The Laws of Motion

1. Lecture 8: Forces & The Laws of Motion

2. Questions of Yesterday You must apply a force F1 to begin pushing a crate from rest across the floor, you must apply a force F2 to keep the crate moving at a constant velocity once its in motion. Which statement is true? a) F1 = F2 b) F1 > F2 c) F1 < F2 2) When do action and reaction pairs of forces not cancel one another out? a) when one of the objects is accelerating b) when both objects are accelerating c) never

3. SI Unit of force = Newton 1 N = 1 kg*m/s2 F and a are vectors! Vector equation! F = ma The acceleration a of an object is directly proportional to the net force acting on it and inversely proportional to its mass Fx = max Fy = may Fz = maz Newton’s Second Law a = F/m

4. N Fg Fg’ N’ Free Body Diagrams Diagram of a single object with all the forces acting ON it DO NOT INCLUDE: -Forces that the object exerts on other objects or the Earth -Other objects that the object is in contact with

5. Fg Free Body Diagrams Tennis ball undergoing projectile motion

6. FA 30o Fg Free Body Diagrams Tennis ball while a tennis player is serving it. The player swings his racket, hitting the 60 g tennis ball with a force 60 N at anangle 30o with the horizontal. What is the magnitude and direction of the net force on the ball? What is the resultant acceleration?

7. N q Fg Free Body Diagrams A block sliding down a frictionless inclined plane. q Is the block accelerating? In what direction?

8. + y - x Fgy + x - y Fgx Fg Fgx = Fgsinq Fgy = Fgcosq Free Body Diagrams A block sliding down a frictionless inclined plane. N q q Choose coordinate system to be in direction of incline plane!

9. + y - x Fgy + x - y Fgx Fg Fgx = Fgsinq Fgy = Fgcosq Free Body Diagrams What is the acceleration of the block? N 3 kg 30o q Fx = max Fy = may Fy = may = 0 N - Fgy = 0 Fx = max max = Fgx

10. FBDs and using Newton’s Laws How much do you weigh in a moving elevator? A 60-kg person stands on a scale in an elevator Draw a free body diagram for the person What does the scale read when the elevator is: at rest? b) Ascending with a speed of 2.0 m/s? c) Descending with a speed of 2.0 m/s? d) Ascending with an acceleration of 2.0 m/s2? e) Ascending with an acceleration of 2.0 m/s2?

11. Practice Problem A train has a mass of 5.0*106 kg and is moving at 90 km/h. The engineer applies the brakes, resulting in a net backward force of 2.0*106 N on the train. The brakes are held on for 30.0 s. What is the final speed of the train? b) How far does the train travel in this period?

12. Tension Free Body Diagrams and Newton’s 2nd law only use forces acting directly on an object Draw a free body diagram for the block What about the rope? FA a

13. N T’ FA T Fg Tension Tension = force exerted along a rope 2nd law: ma = T’ + FA = 0 3rd law: T = -T’ Tension at one end of the rope is equal to the other Tension is CONSTANT all along the rope Applied force is acts “directly” on block through the rope

14. Tension: Practice Problem 5 kg 10 kg Find the acceleration of each object and the tension in the rope

15. Objects in Equilibrium When is ∑F= 0? When is a= 0? An object at rest or moving with a constant velocity is in EQUILIBRIUM Conditions for equilibrium: ∑Fx= 0 ∑Fy= 0

16. 40o 40o Objects in Equilibrium Find the tension in the two wires that support the light fixture Conditions for equilibrium: ∑Fx= 0 ∑Fy= 0

17. Questions of the Day You must apply a force F to push your physics book across your desk at a constant velocity. 1a) The net force acting on the book is… a) F b) between 0 and F c) greater than F d) 0 1b) Are other forces acting on the book in the horizontal direction? a) YES b) NO c) not enough information to know 3) A large crate is at rest in the bed of a truck. As the truck accelerates the crate remains at rest relative to the truck. In what direction is the net force on the crate? a) the same direction as the truck’s acceleration b) opposite the direction of the truck’s acceleration c) the net force is zero