Forces and Momentum

1. Forces and Momentum Chapters 4, 5 and 9

2. Force • A push or pull exerted on an object • It causes a change in velocity (and therefore acceleration) • SI unit is a newton (N) • It is a vector quantity (it has magnitude and direction) • 2 types: • Contact forces • Ex. A book on a table • Force fields • Ex. Gravity pulling on a falling apple

3. Free Body Diagrams • A pictorial way to show all the forces acting on an object • Use an arrow for each force on the object • Arrowhead points in the direction the force is exerted • Length of the arrow indicates the magnitude of the force • Remember to choose your coordinate system (which direction is positive and which is negative)

4. Relating Force and Acceleration • More force gives more acceleration • More mass means you need more force to get the same acceleration • So a = F/m or F = am • This is newton’s 2nd law • Acceleration is directly proportional to the force exerted on an object and inversely proportional to the mass of an object

5. Using Newton’s 2nd Law to Calculate Weight • Weight is the force of gravity acting on your mass • Weight changes from location to location, but mass is constant • Fg = mag • ag = 9.8 m/s2 on the surface of the Earth • The unit for weight is a N because it is a force exerted on you by the mass of the Earth (or whatever planet is pulling on you)

6. Net Force • However, when we talk about force with Newton’s 2nd law, we mean NET force • If forces are in the same plane (or dimension) then they can just be added • Remember though, if in opposite directions then one must be negative according to the coordinate system that you’ve established • If the net force on an object is 0, then the acceleration with also be 0 • It is at equilibrium

7. Newton’s 1st Law • When there is no net force acting on an object, it will continue to behave in the same manner • An object at rest stays at rest, an object in motion remains in motion, unless an outside force acts on it • Inertia • The resistance of a body to change • Measured in mass (more mass means more inertia) • A scale measures your weight because the net force on you must be zero (a = 0) • The scale actually measures how hard it has to push back up on you, not how hard you are pushing down • Scale reading are inaccurate when you are accelerating

8. Apparent Weight

9. Friction • The force that opposes motion • 2 types: • Static friction • When an object isn’t moving (v = 0) • Starts at 0 and increase as you push harder until the maximum is exceeded • Kinetic friction • When an object is moving • As long as push equals kinetic friction, the object continues to move at a constant velocity • If an object is moving at a constant velocity (equilibrium), then friction must equal the force of the push (net force = 0) • Not moving is just a special type of equilibrium when v = 0

10. Calculating Friction • Is determined by the material the surface is made of (measured by the coefficient of friction, μs) • Also affected by how hard the materials push against each other (measured by the normal force, FN) • This is always equal to the weight (mg) of the object, but in a direction perpendicular to the surface the object rests on • So, Ff = μs FN

11. Air Resistance (or Drag) • The frictional force the air exerts on a falling object (opposes motion) • Can be altered by the objects mass and surface area • More mass, the more drag that can build up • The more surface area, the quicker the drag builds up • So, heavy, compact objects fall more quickly than light, spread out ones • When air resistance equals an object’s weight, the net force = 0 and the acceleration = 0 (but velocity doesn’t) • This is the terminal velocity of the object

12. Creating Forces • When you push on an object, the object actually pushes back on you in an equal and opposite direction (Newton’s 3rd law) • Forces always occur in pairs of equal magnitude and opposite direction and on 2 different objects that are exerting forces on each other • Ex. A bat hits a baseball, then the baseball must also hit the bat with the same force

13. The Same Force Paradox • If the force on each object is the same, then why don’t they experience the same effect in the collision • Their masses differ, and therefore they undergo different accelerations • If the forces are equal and opposite, why don’t they cancel out to a net force of 0 • Because the forces are on 2 different objects, forces only cancel if they act on the same object

14. Finding Net Force if Vectors Aren’t in the Same Dimension • This can be done graphically using the tip to tail method • As long as the direction and magnitude of a vector remain unchanged, you can move it anywhere • Move the tip of one vector so that it touches the tail of another • Draw an arrow connecting the exposed tail to the exposed tip • The magnitude and direction of this line is the combined effect of the 2 vectors (we call this the resultant)

15. Momentum • The combined effect of an object’s mass and it’s velocity • Unit is kgm/s • A change in momentum is caused by an impulse • A force acting over a time • The longer the time, the less force required to cause the same change in momentum • More impulse results from a bounce than from a solid hit

16. Conservation of Momentum • Can be passed between objects, but cannot be lost • One object can cause another to move after a collision, but it will have to slow down • It’s the momentum that’s conserved, not the velocity • Is a vector since velocity is a vector (the sign matters) • 2 collision types: • Inelastic – the KE for the system changes • Elastic – the KE for the system remains the same pre and post collision