Chapter 12 Forces and Motion GOAL: Students will be able to interpret and apply Newton s three laws of motion and analyze the motion of an object in terms of its position, velocity, and acceleration. Standard: SC.912.P.12.2, SC.912.P.12.3, & SC.912.P.12.4 Students will: Level Scale 4 design experiments mimicking Newton s three laws of motion and solve complex problems involving motion. 3 interpret and apply Newton s three laws of motion and analyze the motion of an object in terms of its position, velocity, and acceleration. 2 summarize the difference among Newton s three laws of motion and identify the equations for each law. 1 list Newton s three laws of motion. The wind pushes against the man and his umbrella. The push from the wind is a force. What Is a Force? How A force do forces is a push affect or the a motion pull that of an object? A acts force on is an a push object or a pull that acts on an object. A force can cause a resting object to move, or it can accelerate a moving object by changing the object s speed or direction. What Is a Force? Measuring Force You may have measured forces using a spring scale. The stretch of the spring in the scale depends on the amount of weight (a type of force) acting on it. What Is a Force? Units of Force One newton (N) is the force that causes a 1-kilogram mass to accelerate at a rate of 1 meter per second each second (1 m/s 2 ). 1 N = 1 kg m/s 2 What Is a Force? Representing Force Arrows can represent a force. The lengths of the arrows show relative amounts of force. 1
Combining Forces How do forces affect the motion of an object? When the forces on an object are balanced, the net force is zero, and there is no change in the object s motion. Combining Forces The net force is the overall force acting on an object after all the forces are combined. Forces in the same direction add together. Forces in opposite directions subtract from one another. When an unbalanced force acts on an object, the object accelerates. Combining Forces Balanced Forces Balanced forces are forces that combine to produce a net force of zero. An unlimited number of individual forces can act on an object to produce a net force of zero. Combining Forces The two groups pull with equal forces in opposite directions. The forces combine to make a net force of zero. Combining Forces Unbalanced Forces An unbalanced force is a force that results when the net force acting on an object is not equal to zero. Combining Forces Forces can add together or subtract from one another. Adding forces 2
Combining Forces Forces can add together or subtract from one another. Combining Forces Forces can add together or subtract from one another. Adding forces Subtracting forces Adding forces Subtracting forces Equal and opposite forces Friction What are the four main types of friction? Friction is a force that opposes the motion of objects that touch as they move past each other. Friction Static Friction Static friction is the friction force that acts on objects that are not moving. Static friction always acts in the direction opposite to that of the applied force. There are four main types of friction: static friction, sliding friction, rolling friction, and fluid friction. Friction Sliding Friction Sliding friction is a force that opposes the direction of motion of an object as it slides over a surface. Sliding friction is less than static friction. Friction A. Static friction the potted tree does not move. B. Sliding friction when the tree moves, sliding friction acts to oppose the direction of motion. 3
Friction Rolling Friction Rolling friction is the friction force that acts on rolling objects. The force of rolling friction is about 100 to 1000 times less than the force of static or sliding friction. Friction Ball bearings in these wheels greatly reduce friction by replacing sliding friction with rolling friction. Friction Fluid Friction Fluid friction opposes the motion of an object through a fluid. Fluid friction acting on an object moving through the air is known as air resistance. Fluid friction increases as the speed of the object moving through the fluid increases. Gravity In what direction does Earth s gravity act? Earth s gravity acts downward toward the center of Earth. Gravity How do gravity and air resistance affect a falling object? Gravity Gravity is a force that acts between any two masses. Gravity is an attractive force. Gravity can act over large distances. Gravity causes objects to accelerate downward, whereas air resistance acts in the direction opposite to the motion and reduces acceleration. 4
Gravity Earth exerts an attractive, downward force on this boulder. The supporting rock exerts an upward force on the boulder. The forces are balanced. Gravity Falling Objects Both gravity and air resistance affect the motion of a falling object. As objects fall to the ground, they accelerate and gain speed. Terminal velocity is the constant velocity of a falling object when the force of air resistance equals the force of gravity. Gravity This flying squirrel takes advantage of air resistance to slow its fall and increase the distance covered in the jump. Projectile Motion Why does a projectile follow a curved path? The combination of an initial forward velocity and the downward vertical force of gravity causes the ball to follow a curved path. Projectile Motion A thrown ball follows a curved path. Projectile motion is the motion of a falling object (projectile) after it is given an initial forward velocity. Air resistance and gravity are the only forces acting on a projectile. Projectile Motion A. Their masses are different, but the blue and green balls fall at the same rate. 5
Projectile Motion A. Their masses are different, but the blue and green balls fall at the same rate. B. The yellow ball is a projectile, following a curved path. Galileo s work helped correct misconceptions about force and motion that had been widely held since Aristotle s time. Aristotle, Galileo, and Newton It took about 2000 years to develop the modern understanding of the relationships between force and motion. Aristotle, Galileo, and Newton Aristotle Aristotle made scientific discoveries through careful observation and logical reasoning. Aristotle incorrectly proposed that force is required to keep an object moving at constant speed. Aristotle, Galileo, and Newton Galileo Galileo Galilei studied how gravity produces constant acceleration. He rolled balls down wooden ramps. He concluded that moving objects not subjected to friction or any other force would continue to move indefinitely. Aristotle, Galileo, and Newton Newton Newton built on the work of scientists such as Galileo. Newton first defined mass and force. He then introduced his laws of motion. 6
Aristotle, Galileo, and Newton Isaac Newton published his work on force and motion in the book entitled Principia. Newton s First Law of Motion How does Newton s first law relate change in motion to a zero net force? According to Newton s first law of motion, the state of motion of an object does not change as long as the net force acting on the object is zero. Newton s First Law of Motion Unless an unbalanced force acts, an object at rest remains at rest. Unless an unbalanced force acts, an object in motion remains in motion with the same speed and direction. Inertia is the tendency of an object to resist a change in its motion. Newton s First Law of Motion This crash sequence illustrates inertia. The test dummy continues its forward motion as the car slows and stops. Newton s First Law of Motion This crash sequence illustrates inertia. The test dummy continues its forward motion as the car slows and stops. Newton s First Law of Motion This crash sequence illustrates inertia. The test dummy continues its forward motion as the car slows and stops. 7
Newton s First Law of Motion This crash sequence illustrates inertia. The test dummy continues its forward motion as the car slows and stops. How does Newton s second law relate force, mass, and acceleration? According to Newton s second law of motion, the acceleration of an object is equal to the net force acting on it divided by the object s mass. The acceleration of an object is directly proportional to the net force acting on it. The acceleration of an object also depends upon its mass. Mass is a measure of the inertia of an object. The acceleration of an object is always in the same direction as the net force. When a net force acts in the direction opposite to the object s motion, the force produces a deceleration. Newton s Second Law An automobile with a mass of 1000 kilograms accelerates when the traffic light turns green. If the net force on the car is 4000 newtons, what is the car s acceleration? Read and Understand What information are you given? 8
Read and Understand What information are you given? Plan and Solve What unknown are you trying to calculate? What formula contains the given quantities and the unknown? Plan and Solve What unknown are you trying to calculate? Plan and Solve Replace each variable with its known value and solve. What formula contains the given quantities and the unknown? Plan and Solve Replace each variable with its known value and solve. Look Back and Check Is your answer reasonable? 9
Look Back and Check Is your answer reasonable? Powerful sports cars can accelerate at 6 m/s 2 or more. Thus, a smaller acceleration of 4 m/s 2 seems reasonable. 1. A boy pushes forward a cart of groceries with a total mass of 40.0 kg. What is the acceleration of the cart if the net force on the cart is 60.0 N? 1. A boy pushes forward a cart of groceries with a total mass of 40.0 kg. What is the acceleration of the cart if the net force on the cart is 60.0 N? 2. What is the upward acceleration of a helicopter with a mass of 5000 kg if a force of 10,000 N acts on it in an upward direction? Answer: a = F/m = 60.0 N/40.0 kg = 1.50 m/s 2 2. What is the upward acceleration of a helicopter with a mass of 5000 kg if a force of 10,000 N acts on it in an upward direction? Answer: a = F/m = 10,000 N/5000 kg = 2 m/s 2 3. An automobile with a mass of 1200 kg accelerates at a rate of 3.0 m/s 2 in the forward direction. What is the net force acting on the automobile? (Hint: Solve the acceleration formula for force.) 10
3. An automobile with a mass of 1200 kg accelerates at a rate of 3.0 m/s 2 in the forward direction. What is the net force acting on the automobile? (Hint: Solve the acceleration formula for force.) 4. A 25-N force accelerates a boy in a wheelchair at 0.5 m/s2. What is the mass of the boy and the wheelchair? (Hint: Solve Newton s second law for mass.) Answer: a = F/m F = m/a = 1200 kg 3.0 m/s 2 = 3600 N 4. A 25-N force accelerates a boy in a wheelchair at 0.5 m/s2. What is the mass of the boy and the wheelchair? (Hint: Solve Newton s second law for mass.) Acceleration depends directly on force and inversely on mass. The same force causes the single cart to accelerate eight times faster than the chain of eight carts. Answer: a = F/m m = F/a = 25 N/0.50 m/s 2 = 50 kg Force Acceleration Force Acceleration Weight and Mass How are weight and mass related? Mass is a measure of the inertia of an object; weight is a measure of the force of gravity acting on an object. Weight and Mass Mass and weight are related but are not the same. Mass is the measure of the amount of material an object contains. Weight is the force of gravity acting on an object. Weight is the product mass and acceleration due to gravity. 11
Weight and Mass W = mg is a different form of Newton s Second Law, F = ma. The value of g in the formula is 9.8 m/s 2. Weight and Mass If an astronaut has a mass of 112 kilograms, what is his weight on Earth where the acceleration due to gravity is 9.8 m/s 2? Weight = Mass Acceleration due to gravity = 112 kg 9.8 m/s 2 = 1100 kg m/s 2 1100 N Weight and Mass On the moon, the acceleration due to gravity is only about one sixth that on Earth. The astronaut weighs only about one sixth as much on the moon as on Earth. The mass of the astronaut is the same on the moon and on Earth. Weight and Mass Astronaut on Earth Mass = 88.0 kg, Weight = 863 N Astronaut on Moon Mass = 88.0 kg, Weight = 141 N When this bumper car collides with another car, two forces are exerted. Each car in the collision exerts a force on the other. Newton s Third Law What is Newton s third law of motion? According to Newton s third law of motion, whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object. 12
Newton s Third Law Action and Reaction Forces The force your bumper car exerts on the other car is the action force. The force the other car exerts on your car is the reaction force. These two forces are equal in size and opposite in direction. Newton s Third Law Suppose you press your hand against a wall. Your hand exerts an action force on the wall. The wall exerts an equal and opposite reaction force against your hand. Newton s Third Law Action-Reaction Forces and Motion A swimmer pushing against the water is an action force. The reaction force acting on the swimmer causes motion through the water. Newton s Third Law Action-reaction forces propel the swimmer through the water. The swimmer pushes against the water, and the water pushes the swimmer. Newton s Third Law Action-Reaction Forces Do Not Cancel For the swimmer, why do the action and reaction forces not cancel each other and produce a net force of zero? Newton s Third Law Action-Reaction Forces Do Not Cancel For the swimmer, why do the action and reaction forces not cancel each other and produce a net force of zero? The action and reaction forces do not act on the same object. 13
Momentum What is needed for an object to have a large momentum? Momentum is the product of an object s mass and its velocity. Momentum An object with large momentum is harder to stop than an object with small momentum. The momentum for any object at rest is zero. An object has a large momentum if the product of its mass and velocity is large. Momentum Mass is measured in kilograms. Velocity is measured in meters per second. Momentum is measured kilogram-meters per second. Momentum Which has more momentum, a 0.046-kilogram golf ball with a speed of 60.0 meters per second, or a 7.0- kilogram bowling ball with a speed of 6.0 meters per second? Momentum Which has more momentum, a 0.046-kilogram golf ball with a speed of 60.0 meters per second, or a 7.0- kilogram bowling ball with a speed of 6.0 meters per second? Momentum golf ball = 0.046 kg 60.0 m/s = 2.8 kg m/s Momentum Which has more momentum, a 0.046-kilogram golf ball with a speed of 60.0 meters per second, or a 7.0- kilogram bowling ball with a speed of 6.0 meters per second? Momentum golf ball = 0.046 kg 60.0 m/s = 2.8 kg m/s Momentum bowling ball = 7.0 kg 6.0 m/s = 42 kg m/s 14
Momentum Which has more momentum, a 0.046-kilogram golf ball with a speed of 60.0 meters per second, or a 7.0- kilogram bowling ball with a speed of 6.0 meters per second? Momentum golf ball = 0.046 kg 60.0 m/s = 2.8 kg m/s Momentum bowling ball = 7.0 kg 6.0 m/s = 42 kg m/s The bowling ball has considerably more momentum than the golfball. Conservation of Momentum How is momentum conserved? A closed system means other objects and forces cannot enter or leave a system. In a closed system, the loss of momentum of one object equals the gain in momentum of another object momentum is conserved. Conservation of Momentum Objects within a closed system can exert forces on one another. According to the law of conservation of momentum, if no net force acts on a system, then the total momentum of the system does not change. Conservation of Momentum In each collision, the total momentum of the train cars does not change momentum is conserved. Conservation of Momentum In each collision, the total momentum of the train cars does not change momentum is conserved. Conservation of Momentum In each collision, the total momentum of the train cars does not change momentum is conserved. 15
Momentum A class studied the speed and momentum of a 0.25-kilogram ball dropped from a bridge. The graph shows the momentum of the ball from the time it was dropped until the time it hit the river flowing below the bridge. Momentum 1. Applying Concepts At what time did the ball have zero momentum? Describe this point in the ball s motion. Momentum 1. Applying Concepts At what time did the ball have zero momentum? Describe this point in the ball s motion. Momentum 2. Using Graphs At what time did the ball have the greatest momentum? What was the peak momentum value? Answer: At t = 0 s; the ball has zero momentum before it is released. Momentum 2. Using Graphs At what time did the ball have the greatest momentum? What was the peak momentum value? Momentum 3. Calculating What is the ball s speed after 1.25 seconds? (Hint: Use the graph and the momentum formula.) Answer: At t = 2.5 s; about 6.5 kg m/s 16
Momentum 3. Calculating What is the ball s speed after 1.25 seconds? (Hint: Use the graph and the momentum formula.) An artist s depiction of a planet s surface shows a world very different from Earth. Certain universal forces are present. Answer: (m)(v) = 3.25 kg m/s v = (3.25 kg m/s)/(0.25 kg) = 13 m/s upward The speed is 13 m/s. Observations of planets, stars, and galaxies strongly suggest four universal forces exist throughout the universe. electromagnetic strong nuclear weak nuclear gravitational Universal forces act over a distance between particles of matter. The particles need not be in contact. Force is affected by the distance between particles. Electromagnetic Forces What force can attract and repel? Electromagnetic Forces Electric and magnetic force are two different aspects of the electromagnetic force. Electromagnetic force is associated with charged particles. Electric force and magnetic force are the only forces that can both attract and repel. 17
Electromagnetic Forces Electric Forces Electric forces act between charged objects or particles. Objects with opposite charges attract one another. Objects with like charges repel one another. Electromagnetic Forces Clothes often acquire electric charges in the dryer. Clothes with opposite charges tend to cling together. Electromagnetic Forces Magnetic Forces Magnetic forces act on certain metals, the poles of magnets, and moving charges. Electromagnetic Forces Magnets have two poles north and south. Two poles that are opposite attract each other. Two poles that are alike repel each other. Electromagnetic Forces A magnetic force of attraction holds the two train cars together. Nuclear Forces What force holds the nucleus together? Two forces, the strong nuclear force and the weak nuclear force, act within the nucleus to hold it together. 18
Nuclear Forces The strong nuclear force overcomes the electric force of repulsion that acts among the protons in the nucleus. The weak nuclear force is involved in certain types of radioactive processes. Nuclear Forces Strong Nuclear Force The strong nuclear force is a powerful force of attraction that acts only on the neutrons and protons in the nucleus. It acts over short distances approximately the diameter of a proton (10 15 m). It is 100 times stronger than the electric force of repulsion at these distances. Nuclear Forces Weak Nuclear Force The weak nuclear force is an attractive force that acts only over a short range. The weak nuclear force acts at about 10-18 meters, less than the range of the strong nuclear force. Gravitational Forces What is Newton s law of universal gravitation? Newton s law of universal gravitation states that every object in the universe attracts every other object. Gravitational Forces Gravitational force is an attractive force that acts between any two masses. Gravitational force depends upon mass and distance. Gravitational Forces Gravity Acts Over Long Distances The gravitational force between two objects is proportional to their masses. Gravitational force decreases with the square of the distance between the objects. Gravity is the weakest universal force, but it is the most effective force over long distances. 19
Gravitational Forces The Earth, Moon, and Tides The moon s inertia acts to move it away from Earth. Earth s gravitational attraction keeps the moon in a nearly circular orbit around Earth. A centripetal force is a center-directed force that continuously changes the direction of an object to make it move in a circle. Gravitational Forces The moon s inertia and the gravitational pull of Earth result in a nearly circular orbit. Gravitational Forces The gravitational pull from the moon produces two bulges in Earth s oceans one on the side of Earth closest to the moon, the other on the side farthest from the moon. As Earth rotates once per day beneath these two bulges, there are two high and two low tides per day on Earth. Gravitational Forces Satellites in Orbit An artificial satellite needs only its inertia and the centripetal force provided by gravity to maintain its orbit. Satellites in a low orbit are slowed by friction with Earth s atmosphere and eventually reenter Earth s atmosphere. Gravitational Forces Uses of Satellites Hundreds of artificial satellites orbit for many functions: monitoring Earth s weather creating detailed radar maps of Earth s surface using telescopes to study space studying Earth s climate receiving and transmitting radio and microwave signals Gravitational Forces Satellites are used to receive and transmit electromagnetic waves over great distances. 20