Force and Motion Some History: The Copernican Revolution with Copernicus, Galileo, Kepler ...

1. Force and Motion • Some History: • The Copernican Revolution with Copernicus, Galileo, Kepler ... • Newton’s Principia: laws of motion • physics and calculus

2. The First Law of Motion (The Law of Inertia) • An object at rest will remain at rest and an object in motion will remain in motion (at constant velocity) unless acted upon by an external force. • An object has a constant velocity unless there is a net force acting on it. • Forces are the “causes” of changes in motion. • forces on an object arise from interactions with other objects. • forces are vectors • the net force on an object is the vector sum of the individual forces acting on that object • The inertia of an object is its resistance to changes in its motion. • Mass is a measure of inertia. • Inertial Frame of Reference: • a frame of reference in which Newton’s Law of Inertia holds • constant velocity! • counter examples: not an accelerating aircraft or a rotating merry go round

3. The Second Law of Motion • The rate of change of momentum with time is proportional to the net applied force and is in the same direction as the net force • momentum= mass x velocity = mv • Force causes acceleration! • Mass is the measure of inertia • Units: 1 Newton = 1N = 1 kg · m/s2 1N ~ 1/4 pound

4. Example: What force is necessary to give a 0.80 kg cart a horizontal acceleration of 1.5 m/s2? What is the acceleration of the cart if only 1/3 of this force is applied to the cart? Example: A fully loaded Lockheed L-1011 has a mass of 2.17E5 kg. When it accelerates at full throttle down a runway, the engines provide a combined force of 753 kN. If the plane starts from rest, how far will it go during the 33.5 s that it takes to liftoff?

5. Weight: the force exerted by earth (via gravity) on an object • In free fall, gravity is the only force acting on the object • F = ma = mg = w • Weight = (mass)(acceleration of gravity) • Example: what is the weight of a two liter soda bottle which has a mass of 2.0 kg?

6. Normal Force: the contact force exerted by the surface of a rigid object Normal Force N Normal Force N weight w weight w Normal means “perpendicular” Normal force prevents object from sinking into surface Example: A large crate of mass m is placed on a frictionless ramp. The ramp makes an angle q with respect to the horizontal. What is the acceleration of the crate? What is the normal force of the ramp on the crate?

7. Newton’s Third Law • “For every action there is an equal and opposite reaction” • For every action (force) there is a reactive force and the action and reaction forces are equal in magnitude and opposite in direction, and act upon different bodies. • If body A exerts a force FAB on body B, then B exerts a force FBA on A so that FAB = - FBA Action/Reaction Forces on an Object reaction force of table on computer reaction force of table on computer force of computer on table weight of computer

8. Example: A 68 kg passenger rides in an elevator that is accelerating upward at 1.00 m/s2. What is the normal force of the floor on the passenger? What is the force exerted by the passenger on the floor of the elevator?

9. Problem Solving Strategies: • Draw a “free body” diagram • all forces on each object are shown • Choose the object to be isolated. Draw it and any geometric aspects are important. Keep it simple! • Draw all forces on that object as vector arrows, approximately to scale and in the correct direction. Label all forces clearly! • Choose a coordinate system and indicate it on the diagram. Shown the positive direction of displacement, velocity, acceleration, etc. Resolve vectors into components as necessary. • repeat for each object in the problem.

10. T (+) T-wA=FA wB-T=FB (+) w A B mA = 15kg mB = 30kg

11. T=FB mB = 30kg (+) B (+) T A mA = 15kg wA -T=FA =mA g-T w

12. Example: A block of mass M is on a frictionless inclined plane joined by a string over a pulley to a suspended mass m. What is the magnitude of the acceleration if the incline is at an angle of 20º from horizontal? Example 4.11 a bit too elaborate...

13. Friction • opposes motion • due to surfaces sticking together • Kinetic Friction: surfaces are moving relative to each other • a.k.a. Sliding Friction • Static Friction: surfaces are not moving relative to each other. • Static Friction prevents stationary objects from moving until sufficient force has been applied. Friction Applied Force • Coefficient of Friction • Frictional forces depend upon • how hard the surfaces are being pressed together • -> force perpendicular to the surface = normal force • the types of surfaces that are in contact • -> coefficient of friction

14. Material conditions m glass on glass clean 0.9 – 1.0 wood on wood clean and dry 0.25-0.5 wood on wood wet 0.2 steel on steel clean 0.58 steel on steel motor oil 0.2 rubber on solids dry 1-4 steel on Teflon clean 0.04 but ... much variation in trial to trial...0 Generally, static is (sometimes little) greater than kinetic Example: A horizontal force of 100 N is applied to a box of books of mass 20 kg resting on a horizontal table. Does the box slide if the coefficient of friction on the table is 0.40? If the box moves, find its acceleration.

15. Equilibrium • Static Equilibrium: no acceleration with bodies at rest. • Dynamic Equilibrium: no acceleration with moving bodies • Equilibrium implies SFi = 0 • so that SFxi = 0 and SFyi = 0 • Stable, unstable and neutral equi. • Example: A child sits on a sled that rests on a snow-covered hill making an angle q to the horizontal. If the coefficient of friction is 0.10, what is the maximum angle at which the sled will remain at rest?

16. 35º 35º Example: A lantern of mass 1 kg is suspended by a string that is joined to two other strings as shown. What is the tension in each string if the top strings make an angle of 35º to the ceiling?

17. Example: A child of mass 30 kg sits on a light swing suspended by a rope of negligible mass. His sister pushes him forward with a horizontal force until the rope is at an angle of 20º from the vertical. What is the tension in the rope and how much horizontal force is required to hold the child in that position?