Observing Motion CHAPTERS 11 & 12 MOTION & FORCES Everything surrounding us is in motion, but it is relative to other object that remain in place. Motion is observed using a frame of reference. Motion is the change of an object s position relative to a reference point. When describing an object s motion, we must indicate the direction of the motion. Distance vs. Displacement Speed and Velocity Along with knowing which direction an object is moving, we need to know how far the object moves. Distance refers to the length of the path of the object. Displacement is the change in the object s position. Displacement must reported using direction. Some objects move faster than others. Speed describes how fast an object moves in a particular amount of time. Speed does not take into account direction. Velocity is the speed of an object in a particular direction.
Calculating Speed To calculate speed, you must measure two quantities: the distance traveled and the time it took to travel that distance. Speed Practice Problem 1 Calculate the average speed of a golf cart that runs 140 meters in 10 seconds. We typically report speed in meters per second (m/s). Most objects do not travel at a constant speed. Instead, we calculate an average speed for the object. speed = distance/time (or v = d/t) Speed Practice Problem 2 A cyclist travels 50.0 kilometers in 2.5 hours. What is the cyclist s average speed in km/h? Speed Practice Problem 3 Calculate the average speed (in km/h) of Charlie if he runs 4 kilometers to the store in 30 minutes. What distance will he run if he maintains his average speed for 1 hour?
Speed Practice Problem 4 An ant can travel approximately 30 meters per minute. How many meters could an ant move in 45 minutes? Speed Practice Problem 5 How much time would it take for the sound of thunder to travel 2000 meters if sound travels at a speed of 330 meters per second? Acceleration and Motion Velocity has both a speed and direction. When an object undergoes acceleration, its velocity changes. Acceleration is the rate at which velocity changes over time. Acceleration may be positive or negative (deceleration). Acceleration could be a change in direction or a change in speed. Calculating Acceleration To find the acceleration of an object moving in a straight line, we need to measure the object s velocity at different times. average acceleration = change in velocity/time a = v/t If the acceleration is small, the velocity increases gradually. Large accelerations show a rapid increase in velocity.
Acceleration Practice Problem 1 A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later when the car is at the bottom of the slope, its speed is 22 m/s. What is the car s average acceleration? Acceleration Practice Problem 2 A car advertisement states that a certain car can accelerate from rest to 70 km/h in 7 seconds. Find the car s average acceleration. Acceleration Practice Problem 3 If a Ferrari, with an initial velocity of 10 m/s, accelerates at a rate of 50 m/s 2 for 3 seconds, what will its final velocity be? Acceleration Practice Problem 4 A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard s average acceleration?
Acceleration Practice Problem 5 A cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. What is his acceleration? Is this acceleration higher than that of a car which accelerates from 0 to 30 m/s in 8 seconds? Motion & Force A force is any action that can change the state of motion of an object. There are 4 fundamental forces in nature. Force of gravity Strong nuclear force Weak nuclear force Electromagnetic force Motion & Force (cont d) Balanced vs. Unbalanced Forces The fundamental forces that we encounter on an everyday basis are the force of gravity and electromagnetic force. The strength of these forces vary. The strong nuclear force is the strongest of the fundamental forces, but is nearly nonexistent when applied to distances larger than the size of an atom. Gravitational and electromagnetic forces act over significantly larger distances, yet are weaker than the strong nuclear forces. Imagine moving a sofa with a friend. A net force if produced when all forces acting on the sofa are combined. Whenever there is a net force acting on an object, the object accelerates in the direction of the net force. If net force = 0, then a = 0.
Balanced vs. Unbalanced Forces (cont d) Balanced forces are forces that result in a net force of 0. Balanced forces cause no change in motion. Unbalanced forces result in a net force > 0. The forces are not completely cancelled. The acceleration proceeds in a direction that is a combination of all forces. Friction is an unbalanced force that acts against motion. Friction is due to the rough surface of every object. There are 2 types of friction: static and kinetic. Static friction occurs between two stationary surfaces. Kinetic friction occurs between two moving surfaces. Friction Friction & Motion Newton s First and Second Laws Friction is necessary for many everyday tasks. Sometimes, we need to increase friction by making surfaces rougher. Other times, we need to reduce friction by making surfaces smoother. English thinker Sir Isaac Newton developed three laws to describe the relationship between motion and force. These three laws are called Newton s laws of motion. Newton s laws apply to a wide range of motion a caterpillar crawling on a leaf, a person riding a bicycle, or a rocket moving in space.
Newton s First Law Imagine sliding a book across a rough surface like carpet. The book will soon come to rest. Imagine the same book sliding on a ice. Due to less friction between the book and the ice, the smaller force must act over a longer time before the book stops. Without friction, the book would keep sliding. Newton s First Law (cont d) Newton s first law states an object at rest stays at rest unless it is acted on. Objects tend to maintain their state of motion. This tendency is called inertia. Inertia is the tendency of an object to resist change in motion unless an outside force acts on a object. Newton s first law is sometimes called the law of inertia. Every object possesses inertia. Mass is a measure of inertia. Smaller masses require less force in order to accelerate. Larger masses require more force in order to accelerate. Inertia is the reason that a plane, car, or bicycle cannot stop instantaneously. When brought to a stop, there are unbalanced backward forces acting to bring you to a stop as well as the vehicle. Inertia Newton s Second Law Newton s first law describes situations where there are balanced forces applied. Newton s second law applies to situations where there are unbalanced forces applied on an object. (net force > 0) Newton s second law states that the unbalanced force acting on an object equals the object s mass times its acceleration. net force = mass x acceleration F = ma
Second Law Practice Problem 1 Zookeepers lift a stretcher that holds a sedated lion. The total mass of the lion and stretcher is 175 kg, and the upward acceleration of the lion and stretcher is 0.657 m/s 2. What force is needed to produce this acceleration of the lion and the stretcher? Second Law Practice Problem 2 What net force is needed to accelerate a 1600 kg automobile forward at 2.0 m/s 2? Second Law Practice Problem 3 A baseball accelerates downward at 9.8 m/s 2. If the gravitational force is the only force acting on the baseball and is 1.4 N, what is the baseball s mass? Second Law Practice Problem 4 A sailboat and its crew have a combined mass of 655 kg. If a net force of 895 N is pushing the sailboat forward, what is the sailboat s acceleration?
Second Law Practice Problem 5 The net forward force on the propeller of a 3.5 kg model airplane is 7.0 N. What is the acceleration of the airplane? Second Law Practice Problem 6 A 1200 kg case has a force of 1500 N from the engine pushing it forward. The car also has a combined frictional force of 1100 N pushing it backward. What is the acceleration of the car? Weight vs. Mass Weight and mass are two different measurements. Weight is the amount of force on an object due to the pull of gravity. On Earth, your weight is the gravitational force exerted on you by Earth. Mass does not change due to gravity. Weight vs. Mass (cont d) We can calculate the weight of an object by using Newton s second law. F = mass x free-fall acceleration due to gravity F = mg (g = 9.8 m/s 2 ) w = mg Weight depends on the gravitational force at that location.
Law of Universal Gravitation Newton also proposed that all objects in the universe attract each other through the force of gravity. This is known as the law of universal gravitation. F = G (m1m2/d 2 ) The force of gravity increases with an increase of mass. The force of gravity decreases as distance between the two objects increases. Free falling describes the motion of an object when only the force of gravity is acting on the object. Free-fall acceleration is directed toward the center of the earth. Neglecting air resistance, all objects falling near Earth s surface accelerate at the same rate regardless of mass (9.8 m/s 2 ). Free Falling Projectile Motion Newton s Third Law When you throw a baseball, the ball tends to have a curved path. The ball has projectile motion. Projectile motion describes the curved path followed by an object that is thrown, launched, or projected near the surface of Earth. Projectile motion has both a horizontal and vertical component. This causes the curved path. Newton s third law is also known as the law of action and reaction. Third law: For every action, there is an equal but opposite reaction. Forces always occur in pairs, but they don t act on the same object. The forces act at the same time.
Newton s Third Law (cont d) Momentum Consider a swimmer swimming in a pool. The action force is the swimmer pushing back water; whereas, the reaction force is the water pushing the swimmer forward. Equal forces don t always have equal effects. Consider a ball falling to the earth. The force applied to Earth = the force applied to the ball. Using 2nd law, Earth s acceleration < the ball s acceleration. Momentum in the amount of motion in a moving object. We can calculate momentum by multiplying mass by velocity. momentum = mass x velocity p = mv Like velocity, momentum does have direction. Momentum Sample Problem 1 Calculate the momentum of a 6.00 kg bowling ball moving at 10 m/s down the alley toward the pins. Momentum Sample Problem 2 An athlete with a mass of 73.5 kg runs with a constant forward velocity of 1.50 m/s. What is the athlete s momentum?
Momentum Sample Problem 3 If a car with a mass of 925 kg has the same momentum as the previous athlete, what is the car s speed? Momentum Sample Problem 4 What is the momentum of a 20 kg toddler in a minivan traveling west at a rate of 22 m/s? Momentum Sample Problem 5 Calculate the momentum of a 16 kg penguin at rest. Momentum Sample Problem 6 Determine the momentum of a 65 kg skateboarder moving forward with a velocity of 3.25 m/s.
Conservation of Momentum The total amount of momentum in an system is conserved. This is the law of conservation of momentum. The total momentum of two or more objects after collision is the same as it was before the collision. This is explained by Newton s third law (action/reaction).