Foundations of Physical Science Unit One: Forces and Motion
Chapter 3: Forces and Motion 3.1 Force, Mass and Acceleration 3.2 Weight, Gravity and Friction 3.3 Equilibrium, Action and Reaction
Learning Goals Explain the meaning of force. Show how force is required to change the motion of an object. Use a graph to identify the relationships between variables. Explain and discuss Newton's second law and the relationship between force, mass and acceleration. Describe how changing the mass of the car affects its acceleration. Draw conclusions from experimental data. Demonstrate qualitatively how friction can affect motion. Explain Newton's third law of motion. Identify action-reaction pairs of forces. Recognize how Newton's third law of motion explains the physics behind many common activities and useful objects.
Vocabulary air friction equilibrium force friction gravity inertia law of conservation of momentum mass momentum newton Newton's 1st law of motion Newton's 2nd law of motion Newton's 3rd law of motion pounds rolling friction sliding friction viscous friction weight
3.1 Force, Mass, and Acceleration
Sir Isaac Newton s Laws of Motion Sir Isaac Newton (1642-1727), an English physicist and mathematician, is one of the most brilliant scientists in history. Before the age of 30, he formulated the basic laws of mechanics, discovered the universal law of gravitation, and invented calculus!
Newton s Laws
Force A push or a pull, or any action that has the ability to change motion Commonly used units: Pounds (lb) Newtons (N): The force that will give an object of mass 1 kg an acceleration of 1 m/s 2
Force Mass A push or pulling action that can change motion The amount of stuff or matter in an object Measured in NEWTONS Measured in KILOGRAMS
Newton s 1 st Law The Law of Inertia Every object continues in a state of rest, or in a state of motion in a straight line at constant speed, unless it is compelled to change that state by forces exerted upon it
Newton s 2 nd Law The relationship between force, mass and acceleration
Force Causes Acceleration Acceleration is directly proportional to net force! 2x the net force = 2x acceleration 3x the net force = 3x acceleration
Mass Resists Acceleration More massive objects are more difficult to accelerate 2x the mass 1/2 the acceleration 3x the mass 1/3 the acceleration Therefore, acceleration is inversely proportional to mass As one gets bigger, the other gets smaller
Newton s Second Law In other words: or m = F/a Or most commonly: F = ma
Balanced and Unbalanced Forces Net Force: the total of all forces acting on an object Vector: an arrow drawn to scale that represents the magnitude and direction of a quantity having both magnitude and direction In this case the quantity is force
Adding and Subtracting Forces
Equilibrium Mechanical equilibrium: when the net force on something is zero Σ F = 0 Static Equilibrium: objects at rest Dynamic Equilibrium: objects moving at constant velocity
Example Consider the gymnast hanging from the rings. If she hangs with her weight evenly divided between the two rings, how would scale readings in both support ropes compare with her weight? The reading on each scale will be half her weight. The sum of the readings on both scales then equals her weight.
The Support Force Why We Don t Fall Through The Floor Support Force = Normal Force Upward force that is equal and opposite to the force of gravity Σ F = 0
Example An airplane flies at constant velocity. In other words, it is in equilibrium. Two horizontal forces act on the plane. One is the thrust of the propeller that pushes it forward. The other is the force of air resistance that acts in the opposite direction. Which force is bigger? Both forces have the same magnitude. Call the forward force exerted by the propeller positive. Then the air resistance is negative. Since the plane in in equilibrium, can you see that the two forces combine to equal zero?
3.2 Weight, Gravity, and Friction
Gravity A force that pulls every mass toward every other mass Earth is the biggest mass; gravity pulls everything toward the center of Earth Depends on mass more mass, more gravity pulls on you
Mass Weight The quantity of matter in an object Measured in kilograms (kg) The gravitational force exerted on an object by the nearest most-massive body (locally, by Earth) Measured in newtons (N) Mass is directly proportional to weight large mass = large weight small mass = small weight 1 kg (mass) = 9.8 N (weight)
Weight and Galileo A legend has it that, around 1587, Galileo dropped two balls from the Leaning Tower of Pisa to see which would fall faster Objects in free fall have equal acceleration But, why are accelerations equal between objects of greater and lesser mass?
Free Fall and Equal Acceleration One object relates to the other: F/m = F/m F/m = g F/m = g C/D = C/D =
Free Fall and Equal Acceleration A falling 10 kg boulder feels 10x the force of gravity (weight) as a 1 kg stone 10x force acting on 10x mass = same acceleration as the smaller force on the smaller mass
Free Fall without Friction (Air Drag)
Friction Occurs when one object rubs against something else Occurs for solids, liquids and gases It always acts in a direction OPPOSITE to motion
Friction Push crate right, friction is left Object falls down through the air, AIR FRICTION (drag) acts upward The amount of friction depends on the kind of material and how much they press together
Example Suppose a high-flying jumbo jet flies at constant velocity when the thrust of its engines is a constant 80,000 N. What is the acceleration of the jet? What is the force of air drag acting on the jet? Zero acceleration because the velocity is constant. The net force has to be zero if a = F/m. Air drag must be equal and opposite to the thrust: 80,000 N.
Air Drag We know that a feather drops more slowly than a coin when dropped in air Air drag affects the feather more In a vacuum the feather and coin drop at the same time With no air drag the force/mass ratio is the same for both
Free Fall with Friction (Air Drag)
Air Drag In reality, air drag is usually NOT negligible for falling objects Acceleration of fall is less Air drag depends on: Speed Surface area
Air Drag Free fall = downward net force is weight With air present the net force is: Weight Air Drag So the equation becomes: a = (weight-air drag)/m Air drag therefore reduces the net force Reduced net force reduced acceleration Eventually the net force becomes zero The falling object no longer accelerates but has reached TERMINAL VELOCITY
What is the acceleration in each diagram? (The skydiver has a mass of 100 kg) 10m/s 2 6m/s 2 2m/s 2 0m/s 2
Example Consider two parachutists, a heavy person and a light person, who jump from the same altitude with parachutes of the same size. Which person reaches terminal speed first? Which person has the greatest terminal speed? The lighter person reaches terminal speed first. The heavy person falls faster and reaches a higher terminal speed.
Example Which person gets to the ground first? If there were no air drag, like on the moon, how would your answers to these questions differ? The heavier person falls faster and will reach the ground first. If there were no air drag, there would be no terminal speed at all. Both would be in free fall and hit the ground at the same time.
Gravity (again) The attractive force from gravity between objects of ordinary mass is incredibly small. You feel weight because the mass of Earth is large enough to create significant gravity forces.
Legend has it Newton saw an apple fall He realized that the force pulling on the apple was the same force pulling on the moon Earth s gravity reaches the moon!
Tangential Velocity Velocity parallel to the Earth s surface The orbit of the moon around the Earth Keeps the moon constantly falling around the Earth instead of directly into it Similar to the paths of the planets around the sun
Centripetal Force A force that makes a body follow a curved path center seeking force
Newton s Law of Universal Gravitation The force of attraction between two objects is directly related to the masses of the objects and indirectly related to the distance between them
Example What happens to the force between two bodies if the mass of one body is doubled? When one mass is doubled, the force between them doubles
Gravity and Distance Gravity gets weaker with distance This is like how light gets dimmer as you move farther away from it As the light spreads out, its brightness decreases When you are 2X as far away, it appears ¼ as bright
Inverse-Square Law The intensity gets less as the inverse square of the distance The greater the distance from Earth s center, the less the gravitational force on an object
3.3 Equilibrium, Action and Reaction
Newton s Third Law of Motion For every action force, there is a reaction force equal in strength and opposite in direction Action-Reaction Pairs To every action there is always an equal yet opposite reaction
Example When a heavy football player and a light one run into each other, does the light player really exert as much force on the heavy player as the heavy player exerts on the lighter one? Yes, the forces have equal strength
Example Is the damage to the heavy player the same as the damage to the lighter one? No! Although the forces are the same on each,the effects of these equal forces are quite unequal!
Cannon-Cannonball Example Cannonball: F/m = a Cannon: F/m = a Cannonball: smaller mass, greater acceleration
Momentum Inertia in motion momentum = mass x velocity P = mv When direction is not an important factor: momentum = mass x speed, still P = mv
Momentum Momentum (kg-m/sec) P = mv velocity (m/sec) mass (kg)
Momentum A compact car traveling at 20 mph has less momentum than a large truck traveling at the same velocity Why? The truck has more mass
Example When would a car and a truck with 2X car s mass have the same momentum? They d have the same momentum if the car were traveling 2x as fast as the truck (m x 2v) car = (2m x v) truck
How Does Momentum Change? mass changes velocity changes both mass and velocity change Usually-velocity changes (it accelerates!)
Impulse force x time Change in momentum Ft change in mv Ft = mv
Impulse = Momentum Ft = mv (Kg)(m/s 2 )(s) = (kg)(m/s)
Example: Long-Range Cannons Long barrels Longer the barrel, the greater the velocity of the emerging cannonball or shell The force of exploding gunpowder in a long barrel acts on the cannonball for a longer time Increased impulse greater momentum
Momentum Over a Long Time The brakes in your car fail! Do you aim the car at the concrete wall or at the haystack? Either way your momentum decreases the same-you come to rest Hitting the haystack extends your contact time-the time during which your momentum is brought to zero
Momentum Over a Long Time Reduces the force Decreases the resulting deceleration Time of contact is extended 10x force of contact is reduced 10X When you jump you bend your knees before you make contact with the ground: increases the amount of time in the collision
Examples Extending the time in which momentum is being reduced Bungee Jumping The long stretch of the cord results in a small average force to bring the jumper to a safe halt before hitting the ground Catching A Fastball The hand is initially forward so it can move backward after contact with the ball
Momentum and Airbags Airbags expand from the steering wheel/dashboard A sensor has been triggered due to a sudden IMPULSE or CHANGE IN MOMENTUM The airbag fills with nitrogen gas in 1/20 th of a second The airbag expands before the person hits it After 0.3 sec, the collision should be complete and the airbags empty
What is the function of an airbag? During front-end collisions the driver and passengers have inertia and will continue forward until the dashboard, seatbelt, or airbag forces them to stop Airbags were created to cushion the impact by increasing the time to stop, resulting in a smaller force
Momentum Over a Short Period Short contact time = large force Momentum is quickly reduced Example: Karate Expert The impulse is the force of his hand against the bricks multiplied by the time his hand makes contact Therefore the force is huge! If his hand bounces, the force is even greater
Conservation of Momentum There is a fixed amount of momentum for the entire universe Additional momentum cannot be gained or lost, but only transferred from one object to another Momentum is a vector quantity (magnitude and direction)
Law of Conservation of Momentum In the absence of an external force, the momentum of a system remains unchanged M g v g = m b V b (4kg) v g = (0.010kg) (300 m/s) 4v g = 3 v g = 3/4 v g = 0.75 m / s
Momentum is Conserved in Collisions Net momentum before collision = Net momentum after collision mv before = mv after
Elastic Collisions A collision in which colliding objects rebound without lasting deformation or the generation of heat The first ball comes to rest and the second ball moves away at the velocity of the first ball. Momentum is transferred from the first ball to the second one! [m 1 v 1 + m 2 v 2 ] before = [m 1 v 1 + m 2 v 2 ] after
Inelastic Collisions A collision in which the colliding objects become distorted, generate heat, and possibly stick together [m 1 v 1 + m 2 v 2 ] before = [(m 1 + m 2 )v] after
FORMULAS force --> F = ma weight --> F = mg mass --> m = F/a acceleration --> a = F/m Newton s Law of Gravitation --> F = G m 1 m 2 r 2 Momentum = mass x velocity Impulse = force x time Impulse = change in momentum --> Ft = Δ mv Conservation of Momentum --> mv before = mv after Elastic Collision Inelastic Collision [m 1 v 1 + m 2 v 2 ] before = [m 1 v 1 + m 2 v 2 ] after [m 1 v 1 + m 2 v 2 ] before = [(m 1 + m 2 )v] after