Force and Motion Learning Goals: Differentiate between scalars (distance, speed) and vectors (displacement, velocity) Explain the relationship between acceleration and velocity Define g, the acceleration due to gravity Describe and understand centripetal acceleration Understand projectile motion Understand and apply the three laws of Newton and the law of Universal gravitation Explain the conditions for the conservations of linear and angular momenta

Motion To describe completely the motion of an object you need to know three things Position (at one single time) Cartesian coordinates Needs a reference point Velocity Speed (scalar) AND direction → VECTOR Acceleration Magnitude (scalar) AND direction → VECTOR

Scalar VS Vector Scalar: magnitude (and units, of course!) Ex.: your mass, the temperature, SPEED, distance, etc. Vector: magnitude (and units) AND DIRECTION! Ex.: velocity, force, displacement, etc. Are represented by arrows Length proportional to the magnitude Arrowhead indicates the direction

Moving from place to place Speed: SCALAR Average speed = Distance Traveled/time to travel OR Ex.: 2h to go to L.A. (180km), 4h to come back Average Speed = (180[km]+180[km])/(2[h] + 4[h]) = 60 [km/h] Instantaneous Speed: speedometer reading Velocity: VECTOR Average velocity = displacement / time to travel Displacement: straight line distance between starting and ending point, with direction pointing towards the end point. Ex.: 2h to go to L.A. (180km), 4h to come back Average velocity = 0[km] / (2[h]+ 4[h]) = 0 [km/h] !!! Instantaneous velocity = speedometer reading + direction!!!

Displacement is a vector quantity between two points Displacement is a vector quantity between two points. Distance is the actual path traveled.

Special Case: Constant Velocity If the velocity is constant then The speed is not changing The direction is not changing (i.e. straight line motion!) We choose one direction to be +, the other to be – Ex. At a track meet, a runner runs the 100.m dash in 15s. What was the runner’s average speed? Average velocity?

Acceleration If the velocity changes, there is acceleration Change in MAGNITUDE and/or the DIRECTION Ex. : car slowing down or speeding up, the Earth around the Sun, a ball falling down Average acceleration = change in velocity/ time for change = vo = starting velocity vf = ending velocity The UNITS of acceleration are (m/s)/s = m/s2

Acceleration (cont’d) Acceleration is a vector Magnitude: rate at which the velocity is changing Direction: how is the velocity changing If velocity and acceleration are in the same direction, the speed INCREASES If velocity and acceleration are in opposite direction, the speed DECREASES

Which of these car is accelerating? A car on a circular race track going at a constant speed A car coasting to a stop A and B None of these car is accelerating.

Special Case: gravitational acceleration g Objects falling at the surface of the Earth ALL fall with the same acceleration g=9.80m/s2, down Without the effect of AIR resistance = free fall Dropping: Distance fallen = t = time for falling

A ball is dropped from a tall building. How far does the ball drop in 0.50 s?

Throwing a ball up, letting it fall down… There is gravitational acceleration (ALWAYS DOWN) when the ball goes up as well as when it comes down Way Up: acceleration opposite velocity so SLOWING DOWN Way Down: acceleration same direction as velocity so SPEEDING UP

Uniform Circular Motion Constant speed BUT direction is changing all the time! There is an ACCELERATION!!! Points towards the center of the circular path Called Centripetal Acceleration ac ac= v = speed, r = radius of the circular path

If you cut the string, the ball will continue in a straight line. The string keeps the ball in circular motion.

Uniform Circular Motion (cont’d) Ex.: A person drives a car around a circular racetrack with a radius of 70.m at 10.m/s. What is the acceleration of the car?

Projectile Motion Any object thrown by some means Golf ball, tennis ball, football, bullet, etc. The HORIZONTAL (parallel to the ground) and VERTICAL (perpendicular to the ground) motions are INDEPENDANT

Gravity with high speed A zookeeper wants to feed a banana to the monkey with his cannon. The monkey always let go of the branch when the banana is shot. Where should he aim: above, below or on??? If there were no gravity Gravity with slow speed Aiming above the monkey’s head

Forces and Net Force Forces are CAPABLE of producing a change in velocity. ONLY if the force is unbalanced Forces are VECTORS If there is a net, or unbalanced, force: the motion will CHANGE! There will be an acceleration

Laws of Newton An object will remain at rest or in uniform motion in a straight line unless acted on by an external, unbalanced force. The greater the mass of an object, the harder it is to change its motion : INERTIA An object doesn’t need a force to keep on moving!!! Examples of forces? Apart from gravity, in your daily lives, force is transmitted through contact

An elevator is being lifted up an elevator shaft at a constant speed by a steel cable. Forces on the elevator are such that: The upward force by the cable is greater than the downward force of gravity The upward force by the cable is equal to the downward force of gravity The upward force by the cable is smaller than the downward force of gravity None of the above.

An object keeps on moving the way it was UNLESS a force acts on it… Explain those Examples using Newton’s first law: Blood rushes from your head to your feet while quickly stopping when riding on a descending elevator. The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface. To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then abruptly halted. Headrests are placed in cars to prevent whiplash injuries during rear-end collisions. While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting a curb or rock or other object which abruptly halts the motion of the skateboard.

Fnet = ma Unbalanced Force = mass × acceleration OR For the same force acting on difference object, the heavier the object, the smaller the acceleration. For a given object, the larger the force acting on it, the larger the acceleration. Different objects will have the same acceleration if a force proportional to their mass is applied on them…

A net external force of 21 N is applied to a mass of 3. 0 kg A net external force of 21 N is applied to a mass of 3.0 kg. From Newton’s 2nd law, what will be the resulting acceleration? 63 m/s2 21 m/s2 7.0 m/s2 Zero.

Centripetal Acceleration: caused by a FORCE!

For every action there is an equal and opposite reaction. Force always come in pair, acting between two different object!!! The Earth attracts you towards it by gravity, you attract it towards YOU with the same force. When a train and a Beetle collide, the train AND the Beetle will have the same force hitting them. When you walk, you push on the ground BACK and the ground reacts by pushing you FORWARD with the same force. Recoil from a fired riffle: the bullet is pushed forward with the same force that pushes back on the riffle. If you are stranded in space with nothing… you are dooooomed!

A large truck breaks down out on the road and receives a push back into town by a small compact car. While the car, still pushing the truck, is speeding up to get up to cruising speed: The amount of force with which the car pushes on the truck is equal to that with which the truck pushes back on the car The amount of force with which the car pushes on the truck is smaller than that with which the truck pushes back on the car. The amount of force with which the car pushes on the truck is greater than that with which the truck pushes back on the car Neither the car nor the truck exert any force on the other.

A large truck breaks down out on the road and receives a push back into town by a small compact car. After the car reaches the constant cruising speed at which its driver wishes to push the truck: The amount of force with which the car pushes on the truck is equal to that with which the truck pushes back on the car. The amount of force with which the car pushes on the truck is smaller than that with which the truck pushes back on the car. The amount of force with which the car pushes on the truck is greater than that with which the truck pushes back on the car. Neither the car nor the truck exert any force on the other.

Newton’s Law of Gravitation FG = Force of gravity G = 6.67x10-11 Nm2/kg2 m1 and m2: the TWO masses that are attracting each other r: the distance between their centers

What would the force of gravity be between: the Earth and an apple of 0.25kg on a table? the Earth and a football player of 85kg on a football field? the Earth and a 1250kg elephant at the Wild Animal Park? The Earth and a 85kg astronaut in the Space Station 400km above ground? 2.5N 830N 12300N 740N Mass Earth = 5.97424e24kg Radius earth = 6378.1e3m

Linear and Angular momenta Linear momentum p = mv → vector! m: mass, v: velocity Angular momentum L = mvr → vector! m: mass, v: velocity, r: separation with center These two quantities will remain constant for a group of objects UNLESS an EXTERNAL UNBALANCED force is applied to them.

Linear momentum Pi = Pf = 0 (for man and boat) When the man jumps out of the boat he has momentum in one direction and, therefore, so does the boat, but in the opposite direction. Their momenta must cancel out! (= 0)

Angular Momentum force that can create rotation: force that can generate torque If there are no torques acting on an object, the angular momentum is conserved (L doesn’t change).

L = mrv Planets are in elliptical motion around the Sun Sometimes they are closer (r gets smaller) and sometimes they are further (r gets larger) from the Sun.

L = mrv

Homework Chapter 2 Chapter 3 Short-answer questions Exercises 4, 7, 10, 18 Exercises 2 Chapter 3 1, 8, 9, 20 2, 4