Foundations of Physics CPO Science Foundations of Physics Chapter 9 Unit 2, Chapter 5

Unit 2: Motion and Force in One Dimension Chapter 5: Newton's Laws: Force and Motion 5.1 The First Law: Force and Inertia 5.2 The Second Law: Force, Mass, and Acceleration 5.3 The Third Law: Action and Reaction

Chapter 5 Objectives Describe how the law of inertia affects the motion of an object. Give an example of a system or invention designed to overcome inertia. Measure and describe force in newtons (N) and pounds (lbs). Calculate the net force for two or more forces acting along the same line. Calculate the acceleration of an object from the net force acting on it. Determine whether an object is in equilibrium by analyzing the forces acting on it. Draw a diagram showing an action-reaction pair of forces. Determine the reaction force when given an action force.

Chapter 5 Vocabulary Terms force inertia law of inertia Newton’s first law net force dynamic equilibrium static Newton’s second law locomotion newton (N) action reaction Newton’s third law

5.1 The First Law: Force and Inertia Key Question: How does the first law apply to objects at rest and in motion? *Students read Section 5.1 BEFORE Investigation 5.1

5.1 Force Force is an action that can change motion. A force is what we call a push or a pull, or any action that has the ability to change an object’s motion. Forces can be used to increase the speed of an object, decrease the speed of an object, or change the direction in which an object is moving.

5.1 Inertia Inertia is a term used to measure the ability of an object to resist a change in its state of motion. An object with a lot of inertia takes a lot of force to start or stop; an object with a small amount of inertia requires a small amount of force to start or stop. The word “inertia” comes from the Latin word inertus, which can be translated to mean “lazy.”

5.1 Newton's First Law Can you explain why the long table would make the trick hard to do?

5.2 Newton's Second Law The acceleration of an object is equal to the force you apply divided by the mass of the object.

5.2 Newton's Second Law If you apply more force to an object, it accelerates at a higher rate.

5.2 Newton's Second Law If an object has more mass it accelerates at a lower rate because mass has inertia.

5.2 Newton's Second Law a = F m Force (newtons, N) Acceleration (m/sec2) Mass (kg)

5.2 Newton's Second Law Three forms of the second law:

5.2 Calculate acceleration A cart rolls down a ramp. The cart has a mass of 500 grams (0.5 kg). Using a spring scale, you measure a net force of 2 newtons pulling the car down. Calculate the acceleration of the cart. 1) You are asked for acceleration (a). 2) You are given mass (m) and force (F). 3) Newton’s second law applies. a = F/m 4) Plug in numbers. Remember that 1 N = 1 kg·m/sec2. a = (2 N) / (0.5 kg) = (2 kg·m/sec2) / (0.5 kg) = 4 m/sec2

5.2 Calculate acceleration Three people are pulling on a wagon applying forces of 100 N,150 N, and 200 N. The wagon has a mass of 25 kilograms. Determine the acceleration and the direction the wagon moves. 1) You are asked for the acceleration (a) and direction. 2) You are given the forces (F) and mass (m). 3) The second law relates acceleration to force and mass (a = F ÷ m). 4) First, assign positive and negative directions. Next, calculate net force. Finally, use the second law to determine the acceleration from the net force and the mass. 5) F = -100N - 150 N + 200N = -50N a = (-50 N)÷(25 kg) = -2 m/sec2. The wagon accelerates 2 m/sec2 to the left.

5.2 Calculate force An airplane needs to accelerate at 5 m/sec2 to reach take-off speed before reaching the end of the runway. The mass of the airplane is 5,000 kilograms. How much force is needed from the engine? 1) You asked for the force (F). 2)You are given the mass (m) and acceleration (a). 3) The second law applies. F = ma 4) Plug in numbers. Remember that 1 N = 1 kg.m/sec2. F = (5,000 kg) x (5 m/sec2) = 25,000 N

5.2 Calculate force A tennis ball contacts the racquet for much less than one second. High-speed photographs show that the speed of the ball changes from -30 to +30 m/sec in 0.006 seconds. If the mass of the ball is 0.2 kg, how much force is applied by the racquet? 1) You are asked for force (F). 2) You are given the mass (m), the change in speed (V2 - V1), and the time interval (t). 3) Newton’s second law (F = ma) relates force to acceleration. Acceleration is the change in speed divided by the time interval over which the speed changed (a = (V2-V1) / t). 4) Use the change in speed to calculate the acceleration. Use the acceleration and mass to calculate the force. 5) a = (60 m/sec) ÷ (0.006 sec) = 10,000 m/sec2 F=(0.2 kg) × (10,000 m/sec2) = 2,000 N. This force is equal to three times the weight of the tennis player and 1,000 times the weight of the tennis ball.

5.2 Equilibrium The condition of zero acceleration is called equilibrium. In equilibrium, all forces cancel out leaving zero net force. Objects that are standing still are in equilibrium because their acceleration is zero. Objects that are moving at constant speed and direction are also in equilibrium. A static problem usually means there is no motion.

5.2 Calculate force A woman is holding two dogs on a leash. If each dog pulls with a force of 80 newtons, how much force does the woman have to exert to keep the dogs from moving? 1) You are asked for force (F). 2) You are given two 80 N forces and the fact that the dogs are not moving (a = 0). 3) Newton’s second law says the net force must be zero if the acceleration is zero. 4) The woman must exert a force equal and opposite to the sum of the forces from the two dogs. Two times 80 N is 160 N, so the woman must hold the leash with an equal and opposite force of 160 N.

5.2 The Second Law: Force, Mass, and Acceleration Key Question: What is the relationship between force, mass, and acceleration? *Students read Section 5.2 BEFORE Investigation 5.2

5.3 Newton's Third Law “For every action there is an equal and opposite reaction.” This statement is known as Newton’s third law of motion. Newton’s third law discusses pairs of objects and the interactions between them.

5.3 Newton's Third Law The astronauts working on the space station have a serious problem when they need to move around in space: There is nothing to push on. The solution is to throw something opposite the direction you want to move. This works because all forces always come in pairs.

5.3 Calculate force Three people are each applying 250 newtons of force to try to move a heavy cart. The people are standing on a rug. Someone nearby notices that the rug is slipping. How much force must be applied to the rug to keep it from slipping? Sketch the action and reaction forces acting between the people and the cart and between the people and the rug. 1) You are asked for how much force (F) it takes to keep the rug from slipping. 2) You are given that three forces of 250 N are being applied. 3) The third law says that each of the forces applied creates a reaction force. 4) Each person applies a force to the cart and the cart applies an equal and opposite force to the person. The force on the rug is the sum of the reaction forces acting on each person. The total force that must be applied to the rug is 750 N in order to equal the reaction forces from all three people.

5.3 Newton's Third Law Locomotion is the act of moving or the ability to move from one place to another.

5.3 The Third Law: Action and Reaction Key Question: Can you identify action-reaction forces? *Students read Section 5.3 BEFORE Investigation 5.3

Application: Biomechanics