"Chapter 8: Motion and Forces"
Chapter 8: Motion and Forces I. Motion A. Speed and Velocity 1. Motion, the change in position in a reference frame, is measured in terms of the distance traveled by an object from a fixed point. 2. Speed a) how fast an object moves b) measurements needed: distance, time c) the distance traveled divided by the time interval during which the motion occurred 3. Constant Speed is the Simplest Type of Motion a) An object covering equal distances in equal amounts of time is traveling with constant speed. b) Most objects do not move at a constant speed. 4. Speed Can Be Determined from a Distance-Time Graph a) x-axis: time b) y-axis: distance c) Constant/Average Speed is a straight line on a distance-time graph d) The speed can be determined by calculating the slope of the line. e) Steeper line = faster speed 5. Speed is Calculated as Distance Divided by Time a) Average Speed = Distance Time b) Units: km/h, m/s c) Example: A lion moves 15 km in 4.0 hours. What is the lion’s average speed? Average Speed = Distance/Time Average Speed = 15 km/4.0 h Average Speed = 3.75 km/h = 3.8 km/h 6. Velocity Described Both Speed and Direction a) Knowing the speed is not always enough information. b) Often, direction is needed to be able to predict the location of an object. c) Velocity—speed in a given direction d) Examples: 9 m/s east, 13 km/hr towards school, 25 km/h north, etc. e) Example Problem: Find the velocity in m/s of a swimmer who swims exactly 110 m toward the shore in 72 s. f) Solution: v = d/t v = 110 m/72 s v = 1.527 = 1.5 m/s toward shore B. Momentum 1. Which is harder to stop: a train moving at 20 mi/h, or a convertible moving at 20 mi/h? a) The train is harder to stop, because it has more mass 2. Moving Objects Have Momentum a) Momentum—a quantity defined as the product of an object’s mass and its velocity. b) Momentum (p) = Mass (m) x Velocity (v) c) Momentum also has a direction (determined by the velocity) d) Units: kgm/s (kilogram-meters per second) e) Example Problem: A 75 kg speed skater is moving forward at 16 m/s. What is her momentum? f) Solution: p=mxv p = 75 kg x 16 m/s p = 1200 kgm/s g) The more mass an object has, the greater its momentum. h) If an object is not moving, its momentum = 0 3. The Law of Conservation of Momentum a) What happens when a truck crashes into a car? The truck (which has a greater momentum) pushes the car b) The motion will continue in the same direction of the object that had a greater momentum to begin with. c) Law of Conservation of Momentum = The total amount of momentum in a system is conserved. II. Acceleration and Force A. Acceleration—the change in velocity divided by the time interval in which that change occurred 1. Acceleration can mean: a) Speeding Up (positive acceleration) b) Slowing Down (negative acceleration) c) Changing Direction 2. Equation: A = Final Velocity – Initial Velocity = v Time t 3. Example Problem 4. Acceleration can be determined from a velocity-time graph a) x-axis: time b) y-axis: velocity c) Straight line on a velocity-time graph = constant acceleration d) The slope of the line = value of the acceleration e) Positive slope means an object is speeding up; negative slope means an object is slowing down. f) Slope of zero means there is no acceleration a. Horizontal line b. Object traveling at constant speed B. Force 1. Force—the cause of acceleration (a push or a pull) 2. Net Force: a) the combination of all of the forces acting on an object b) determines whether or not the velocity of the object will change (speed up? slow down? change direction?) 3. An object accelerates in the direction of the net force. 4. Balanced Forces do not Change Motion a) Balanced forces are forces acting on an object that combine to produce a net force equal to zero. b) Example: Tug-of-war when the rope isn’t moving; no one is winning. 5. Unbalanced Forces Change Motion a) Unbalanced forces are forces acting on an object that combine to produce a net nonzero force. b) Example: Tug-of-war when the rope is moving; one team is winning, because they are pulling with a greater force. c) Movement occurs in the direction of the larger force. C. Friction and Air Resistance 1. Why does a rolling ball eventually stop? a) Friction—the force between two objects in contact that opposes the motion of either object. b) B/c of friction, a constant force must be applied to an object to keep it in motion. c) Friction can also keep objects that are at rest in place (car parked on a hill). 2. Frictional Force Varies Depending on the Surfaces in Contact a) Frictional forces are stronger when the surfaces are rough. b) Frictional forces are weaker when the surfaces are smooth. 3. Air Resistance is a Form of Friction a) Air resistance—caused by the interaction between the surface of a moving object and the air molecules. b) The amount of air resistance depends on: i. Size and Shape—air resistance increases as surface area increases ii. Speed—air resistance increases as speed increases. D. Gravity 1. Gravity—the force of attraction between two particles of matter due to their mass a) Every object exerts a gravitational force on every other object. b) We just don’t notice it, b/c Earth’s gravity is so much stronger (b/c Earth is so much more massive) 2. Mass and Distance Affect Gravitational Force a) The greater the mass of an object, the greater the gravitational force it exerts on other objects. b) As the distance between two objects increases, the gravitational force between them decreases rapidly. E. Free Fall 1. Free Fall—the motion of a body when only the force of gravity is acting on it. 2. Free-fall Acceleration Near Earth’s Surface is Constant a) Free-fall acceleration results from gravity, so it is abbreviated g and its value is 10.0 m/s2 close to the earth. b) Without air resistance, any two objects dropped together will hit the ground at the same time. c) They fall at the same rate b/c the heavier object has a greater gravitational force, but it is also harder for the earth to accelerate all the extra mass…so it all equals out! III. Newton’s Laws of Motion A. Newton’s 1 Law of Motion st 1. An object at rest remains at rest and an object in motion maintains its velocity unless it experiences an unbalanced force. a) Part 1: Objects at Rest i. An object that isn’t moving won’t start moving until a push or a pull is exerted on it. ii. Example: a golf ball won’t fly through the air until it is hit by a golf club. b) Part 2: Objects in Motion i. An object will stay in motion with the same speed and direction until a push or a pull changes that motion. ii. Example: a person riding in a car that slams on the brakes will move forward until the seatbelt changes their motion. c) Inertia—the tendency of an object to remain at rest or in motion with a constant velocity i. Resistance to changes in motion ii. The more mass an object has, the more inertia it has. iii. Therefore it is easier to change the motion of a less massive object (think: full vs. empty grocery carts) B. Newton’s 2 Law of Motion nd 1. The unbalanced force acting on an object equals the object’s mass times its acceleration. 2. Mathematically, Force = mass x acceleration 3. Units: Force (N), mass (kg), acceleration (m/s2) 4. 1 N = 1 kgm/s2 a) Part 1: Acceleration Depends on Mass i. An object’s acceleration decreases as its mass increases. ii. An object’s acceleration increases as its mass decreases. b) Part 2: Acceleration Depends on Force i. An object’s acceleration increases as the force on it increases. ii. An object’s acceleration decreases as the force on it decreases. C. Weight 1. Weight Equals Mass Times Free-fall Acceleration a) Weight—the force on an object due to gravity b) Since F = m x a, W (force of gravity) = m x g (acceleration due to gravity) c) Weight is measured in Newtons, b/c weight is a force 2. Weight Is Different from Mass a) Mass i. the amount of matter in an object ii. cannot change based on location iii. constant for an object b) Weight i. depends on gravity ii. can change based on location (when the gravity changes) 3. Weight Influences Shape a) Organisms on land must have strong structural parts that can support their mass against the pull of gravity (skeleton, tree trunk, etc.) b) Organisms in water have the downward force of gravity balanced by the upward force of the water, so they don’t require the same structural support. 4. Velocity Is Constant When Air Resistance Balances Weight a) Terminal Velocity—when the downward force of gravity equals the upward force of air resistance and the falling object stops accelerating b) Object has balanced forces (no change in motion) c) This is the object’s maximum velocity. d) Example: sky diver D. Newton’s 3 Law of Motion rd 1. For every action force, there is an equal and opposite reaction force. 2. What would happen if you stood on a skateboard and threw a brick forward? 3. You would get pushed backward. 4. The action force is “you pushing forward on the brick” 5. The reaction force is “the brick pushing back on you” 6. 3rd law states that forces always act in pairs. 7. The force pairs are: a) on different objects b) in opposite directions c) equal in size