Forces and The Laws of Motion Chapter 4

Section 1 Changes in Motion

Section 1 Objectives Describe how force affects the motion of an object Interpret and construct free-body diagrams

Force Force is, an action exerted on an object which changes the object’s state of rest or motion. Force can cause an acceleration The SI unit of force is a Newton (N). A newton is dervived from the units of mass (kg) and acceleration (m/s2). 1 N = 1 kg • m/s2 Clip 310 Forces can act through contact or at a distance. Contact forces result from physical contact between two objects. Pulling a wagon Catching a football Field forces does not involve contact The force of gravity is an example of field force. Clip 512

Force Diagrams Force is a vector. It depends on the magnitude and the direction of the force Diagrams that show force vectors as arrows are called a force diagram. The force vector points in the direction of the force. Its length is proportional to its magnitude Assume that all forces act on the center of the object No matter where the force is applied A free-body diagram helps analyze a situation Used to analyze only the forces affecting the motion of a single object Show clip 566

Force Diagrams Free-Body Diagram Force Diagram Chapter 4 In a force diagram, vector arrows represent all the forces acting in a situation. A free-body diagram shows only the forces acting on the object of interest—in this case, the car.

Drawing Free-body Diagrams Identify the forces acting on the object and the directions of the forces. Draw a diagram to represent the isolated object. Draw and label vector arrows for all external forces acting on the object.

Free-body Diagram Sample Problem Draw a free body diagram for a person pulling a sled. The magnitudes of the forces acting on the sled are 60 N by the string, 130 N by the earth, and 90 N upward by the ground. F ground F string F earth

Today’s Homework Page 124 Page 145 Practice A 1-2 Section Review 1 – 5 7 - 9

Section 2 Newton’s First Law

Section 2 Objectives Explain the relationship between the motion of an object and its net external force acting on the object Determine the net external force acting on an object Calculate the force required to bring an object to equilibrium.

Newton’s First Law An object at rest remains at rest, and an object in motion remains in motion with constant velocity unless the object experiences a net external force. Sometimes referred to as the law of inertia. Inertia is the tendency of an object to resist change in motion. Mass is the measure of inertia Show Clip 589 First Law says that when the net force on an object is zero the objects acceleration is also zero. The sum of the forces acting on an object is the net force. Although several forces are acting on this car, the vector sum of the forces is zero. Thus, the net force is zero, and the car moves at a constant velocity.

Determining Net Force Define the problem, and identify the variables Select a coordinate system, and apply it to the free body diagram Find the X and Y components of all vectors Find the net force in the x and y directions Find the net force.

Sample Problem B Derek leaves his physics book on top of a drafting table that is inclined at a 35° angle. The free body diagram at the right shows the forces acting on book. Find the net force acting on the book. F friction = 11N F table on book = 18 N F gravity on book = 22 N

Equilibrium Equilibrium is the state in which the net force on an object is zero. Objects that are either at rest or moving with constant velocity are said to be in equilibrium. Tip: To determine whether a body is in equilibrium, find the net force. If the net force is zero, the body is in equilibrium. If there is a net force, a second force equal and opposite to this net force will put the body in equilibrium.

Today’s Homework P 128 P 129 P 145 Practice B 1 – 3 1- 4 1 – 6, 10 - 12

Newton’s Second and Third Laws Section 3 Newton’s Second and Third Laws

Section Objectives Describe an object’s acceleration in terms of its mass and the net force acting on it. Predict the direction and magnitude of the acceleration caused by a known net force Identify action-reaction pairs

Newton’s Second Law The acceleration of an object is directly proportional to net force acting on the object and inversely proportional to the objects mass. F = ma Net Force = mass X acceleration Show clip 590

Sample Problem C Roberto and Laura are studying across form each other at a wide table. Laura slides a 2.2 kg book towards Roberto. If the net force acting on the book is 1.6 N to the right, what is the books acceleration? Given: m = 2.2 kg F = 1.6 N to the right Unknown: a = ?

Newton’s Third Law Forces always work in pairs. Newton’s third laws says: If two objects interact, the magnitude of the force on object 1 by object 2 is equal to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction. This is more commonly heard as: For every action there is an equal but opposite reaction.

Third Law con’t. If forces are equal why don’t they cancel each other out? Action-reaction pairs do not imply that the net force on either object is zero. The action-reaction forces are equal and opposite, but either object may still have a net force on it. Consider driving a nail into wood with a hammer. The force that the nail exerts on the hammer is equal and opposite to the force that the hammer exerts on the nail. But there is a net force acting on the nail, which drives the nail into the wood.

Third Law con’t. Remember the forces are acting on different objects. Also there may be a mass difference between the two objects. See Clip 715

Today’s Homework P 132 Practice C 1 – 5 P 134 1 – 5 P 146 13 - 22

Section 4 Everyday Forces

Section Objectives Explain the difference between mass and weight Find the direction and magnitude of normal forces Describe air resistance as a form of friction Use coefficients of friction to calculate frictional force.

Weight Weight is the measure of the force of gravity, Fg. Because of Newton’s 2nd Law, F=ma, we can calculate weight as: Fg = mag Fg – Force of gravity (weight) ag – acceleration due to gravity, 9.8 m/s2

The Normal Force Imagine a television set at rest on a table. Why doesn’t the television set continue to fall through the table? Forces are in equilibrium. But what force opposes the force of gravity? The Normal force. (Fn) A force that acts on a surface in a direction perpendicular to the surface. The normal force is always perpendicular to the surface. See Clip 592 Fn Fg

Normal Force con’t. The normal force is not always opposite of the force of gravity, as shown by the picture of a refrigerator on a ramp. Fn θ θ Fg

The Force of Friction Friction opposes the applied force. There are two types of friction Static friction is a force that resists the initiation of sliding motion between two surfaces that are in contact and at rest. Kinetic friction is the force that opposes the movement of two surfaces that are in contact and are sliding over each other. Kinetic friction is less than static friction The force of friction is proportional to the normal force In a free-body diagram the force of friction is parallel to the surface of contact. Friction can be calculated approximately. See Clip 316

Coefficient of friction The quantity that expresses the dependence of frictional forces on the particular surfaces in contact. It is represented by the Greek letter mu, .

Coefficient of friction con’t. Defined by the ratio of the force of friction to the normal force between two surfaces. The coefficient of kinetic friction: k = Fk/Fn The coefficent of static friction: s = Fs,max/Fn If value of  and the normal force is known then the force of friction can be calculated directly. Ff = Fn

Sample problem D A 24 kg crate initially at rest on a horizontal floor requires a 75 N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor. Given Fs,max = Fapplied = 75 N m = 24 kg s = ? Equation s = Fs,max/Fn Fn = crates weight = mg

Air Resistance Air resistance is a form of friction. Whenever an object moves through a fluid medium, such as air or water, the fluid provides a resistance to the object’s motion. For a falling object, when the upward force of air resistance balances the downward gravitational force, the net force on the object is zero. The object continues to move downward with a constant maximum speed, called the terminal speed.

Fundamental Forces There are four fundamental forces: Electromagnetic force Gravitational force Strong nuclear force Weak nuclear force The four fundamental forces are all field forces.

Today’s Homework P139 Practice D 1 – 3 P143 1 – 5