What causes acceleration?

1. What causes acceleration? straight line (line of site) the monkey begins to fall ad the precise moment when the ball leavesthe barrel of the gun The ball and the monkey arrive at the point marked by the red dot at the same time path of bullet path of monkey

2. What causes acceleration? Analysis First, imagine what would happen in the absence of gravity ObjectExternal InfluenceMotion monkey none “floats” in place ball none straight line with constant speed Result: ball hits monkey ObjectExternal InfluenceMotion monkey gravity uniform acceleration toward ground ball gravity sideways at constant speed + downward with uniform acceleration Result: ball hits monkey It’s very useful to consider motion without the effects of gravity!

3. What causes acceleration? • Aristotle: forces cause velocities • Galileo: “external influences” • Newton: “unbalanced force” • For now we define force according to its effect on the motions of things • the operational definition we find is concisely expressed by three (3) simple rules • First we examine how forces act – then we look at a restatement of the rules • Preliminary Issue: mass, weight and what they mean to freely falling monkeys • Mass • 1. a measure of how much matter is in an object.. literally proportional to the number and size of atoms in the object • 2. a measure of the internal resistance of an object to a change in its motion…perhaps you could think of it as a measure of the objects “desire” to remain in motion at a constant speed in a straight line.

4. What causes acceleration? Mass * mass is an intrinsic property of an object – to change the mass of an one must make a change (physical, chemical, or nuclear) in the object * in order to make two objects accelerate at the same rate one must pull or push harder on the more massive object In the monkey demonstration (and in Galileo’s law of falling) we observe that objects under the influence of gravity alone fall with equivalent rates of acceleration objectExternal InfluenceAcceleration monkey force of gravity (weight of monkey) 10 m/s2 ball force of gravity (weight of ball) 10 m/s2 grain of sand weight of grain of sand 10 m/s2 dump truck weight of dump truck 10 m/s2 let’s look at this…………….

5. What causes acceleration? objectresistance to accelerationExternal InfluenceAcceleration monkey mass of monkey weight of monkey 10 m/s2 ball mass of ball weight of ball 10 m/s2 grain of sand mass of grain of sand weight of grain of sand 10 m/s2 dump truck mass of dump truck weight of dump truck 10 m/s2 acceleration of the stuff (the motional reaction) external influence on the stuff amount of stuff • Conclusion: There must be a direct proportionality between weight and mass but, same acceleration!! greater influence of weight force more mass

6. What causes acceleration? By analyzing free-fall we conclude that: AND that the weight force is proportional to the mass: twice as much mass mass weight twice as much weight same ratio

7. What causes acceleration? The genius of Newton and the power of explanation Newton: gravity is only one type of force (what about friction, pushing pulling, electric attraction or repulsion…) gravity is “special” in the sense that gravitational force (a.k.a. weight) is proportional to mass Nevertheless, whenever any net force acts upon any mass to cause any acceleration, the rule is: NET FORCE = MASS X ACCELERATION F = m a F3 F2 F1 a force exerted on the object an object another force exerted on the object the meaning of “net” force: IF: acceleration (F3 = F4) F2 > F1 to the right (F3 = F4) F1 > F2 to the left (F3 = F4) F1 = F2 none (i.e. straight line at constant speed) NOW YOU TRY!! 4

8. Net Force When forces balance, there is equilibrium. F1 = Force felt by Bo because of Diddley. F2 = Force felt by Diddley because of Bo. F1 = F2 F1 F2 Bo Diddley

9. What causes acceleration? Force is a vector quantity! TOTALNET FORCEON AN OBJECT MASS OF THE OBJECT ACCELERATION OF OBJECT CAUSED BY NET FORCE X = expressed in “Newton's” [N] expressed in “kilograms” [kg] expressed in “meters per second, per second” m/s2 mass say F1 > F2 then (F1 – F2) = mass x acceleration = ma F1 F2 acceleration for F1 > F2

10. What causes acceleration? The “Newton” is the standard measure of force in the system we use. Push on a 1 kilogram MASS with a FORCE of 1 Newton then the object will ACELLERATE at a rate of 1 m/s2 in the direction of the force….provided that the force is not “balanced” by another force on the object. If your body contains 75 kg of mass then… on earth you weigh (force) about 75kg X 10 m/s2 = 750 Newtons acceleration mass • Some examples • Mass and weight • (a) in free-fall on Earth acceleration = 10 m/s2 10 kg weight net force = mass X acceleration a 10 kilogram block has a weight on Earth of 100 N!

11. F = contact force exerted by table on the block W = weight force exerted by the Earth on the apple acceleration = 10 m/s2 1 kg weight 1 kg weighs 10 Newtons on Earth Convert to lbs= 1 kg weighs about 2.2 lbs 2. sitting on a table on Earth What forces are acting on the apple? 1 kg Net force upward mass acceleration = X F – W = 1 kg X 0 m/s2 F – W = 0 Newtons for the acceleration to be equal to zero the forces must be balanced If two forces act in opposite directions, the net force is in the direction of the larger force and is equal to the difference between the larger and smaller force F = W = 1 Newton

12. Fair = force of air resistance exerted BY air on block 3. skydiving 10 kg acceleration W = weight force exerted by Earth ON block • If Fair = 60 Newtons at what rate does the block accelerate? • First find the “NET FORCE” : W-Fair • What’s the weight? W = mass X g = 10 kg X 10 m/s2 = 100 N • NET FORCE = 100 N – 60 N = 40 N • NET FORCE = MASS X ACCELERATION • 40 N = 10 kg X ACCELERATION • 3. Solve for acceleration:

13. Terminal velocity – The speed at which air resistance (aka drag) matches the pull of gravity,resulting in a constant fall rate. What is the net force on a skydiver as she falls at terminal speed? NET FORCE = MASS x ACCELERATION Fait – W = M x A Fait – W = M x 0 = 0 Fait – W = 0 What is the force of air resistance on a skydiver whose mass is 40 kilograms when she falls at terminal speed? NET FORCE = ZERO Fait – W = 0 Fair = W = 40kg X 10 m/s2 Fair = force of air resistance exerted BY air on block 40 kg acceleration = 0 W = weight force exerted by Earth ON block

14. Laws of Motion 1. Newton’s 1st Law: An object at rest, remains at rest, OR if in motion, travels in a straight line at constant velocity, UNLESS acted on by a net force.

15. Laws of Motion • 2. Newton’s 2nd Law: For a body having constant mass, M, the NET FORCE APPLIED to the body, the Mass of the body, and the observed Acceleration of the body are related by: • FORCE = MASS X ACCELERATION • F = MA A 2 kg mass is acted on by a 2 N force. What is its acceleration? a = 2 N / 2 kg = 1 m/s2 What if a 0.5 N frictional force was also in place? a = (2 - 0.5 N)/2 kg = 0.75 m/s2 F = 2N 2 kg F = 2N f = 0.5 N 2 kg

16. Laws of Motion • Newton’s 3rd Law: For every action there is an equal and opposite reaction. – rule of force pairs • Objects can not act on one another without being acted upon. • When you strike a wall, does it hurt your hand? You might say the wall struck you. Newton would say the force you applied to the wall was the same as that which the wall applied to you. The wall is bigger and more massive, therefore has more inertia and was not harmed as much as you. frictional force from wall If you push on a wall, the wall pushes back on you. It does so with a force equal in strength to the one you exert on it! Reaction force from wall Applied Force “Pushing” Weight

17. The “rule of force pears” For every force exerted ON an object, the object exerts an equal and oppositely directed force ON its environment Force on Rock from Earth = Force on Earth from Ball a = F/m = gRock acceleration a = F/mEarth’s acceleration

19. Gravity

20. Gravity contact force exerted by table on the apple contact force exerted by the apple on the table force of Earth on the apple force of apple on the Earth