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Chapter Study Guide; Chapter 4 Dynamics: Newton’s Laws of Motion Chapter Goals After studying the material of the chapter, the student should be able to: State Newton’s three laws of motion and give examples that illustrate each law. Explain what is meant by the term net force. Use the methods of vector algebra to determine the net force acting on an object. Define each of the following terms: mass and weight, and distinguish between mass and weight. Identify the SI units for force, mass, and acceleration. Draw an accurate free body diagram locating each of the forces acting on an object or a system of objects. Use free body diagrams and Newton’s laws of motion to solve word problems. New Vocabulary Dynamics Net force Newton’s first law Newton’s second law Newton’s third law Weight Friction Coefficient of friction Normal Force Principles of Physics Newton’s Laws of Motion Newton’s three laws of motion describe the nature of forces and their effect on mass. Forces are the pushes and pulls that are the cause for acceleration. Forces are vectors. As with 2D motion, when forces act in two dimensions, the forces can be broken into perpendicular components and the motion which results from the component forces can be studied separately. Forces add like vectors, and the sum of all forces on an object is known as the net force. The acceleration of an object is proportional to the net force and in the same direction as the net force. The acceleration is inversely proportional to the mass of the object. By their nature, forces are vectors that come in pairs. These paired forces act on different objects, point in opposite directions, but have the same magnitude. Force of Gravity The force of gravity which acts on an object near the surface of the Earth is also known as the weight of the object. The force of gravity always acts to pull the object toward the center of the earth and has a magnitude of 9.8m/s2 times the mass of the object. Normal Force The normal force is an adaptive contact force that acts between two objects. The direction of the normal force is perpendicular to the plane of contact and the magnitude can vary from zero to any value depending on other forces acting perpendicular to the plane of contact. Tension Forces Tension is a force transmitted by a rope. This force is like a contact force, but is a “pull” rather than a “push”. If the rope is light enough to be considered massless, the tension is the same on both sides of a rope. Friction Forces Friction is a contact force that acts parallel to the surface of contact between two objects. The magnitude of the force depends on the relative motion of the surfaces, the nature of the surfaces, and the normal force between the surfaces. When the objects are at rest, static friction takes the appropriate value to balance out other forces which act parallel to the surface of contact. If the sum of the other forces exceeds a maximum value μS times FN, the force of static friction is overcome and the object will accelerate. When the objects are in motion, kinetic friction takes a constant value of μ S times FN and points opposite the direction of motion. Equations Formula Variables Descriptions Newton’s first law Net F 0 or F 0 Newton’s second law a F /m or F m a Newton’s third law F12 F 21 Weight w mg F fr F N Force of friction Dimensional Analysis Problem Solving Strategies Free-body diagrams A free-body diagram is a sketch that includes all of the forces acting on a single object to be studied. The axes of the reference frame are included and any vectors which do not point along the axes are broken into components. A net force is typically included. Each object FNet being studied should have a separate free body diagram. Solving for the net force If the magnitude and direction of all forces acting on an object are known, the net force can be found as the vector sum of all the forces. Break the vectors into components along the appropriate axes, add the components, and reconstruct the net force vector. Solving for an adaptive force The normal force and the force of static friction are adaptive forces; they can change their magnitude to maintain an object in its state of rest. To solve for the magnitude of this force, find the total of all parallel (perpendicular) forces. The force of static friction (normal force) is the opposite of this total. Solving systems coupled by a string If two objects are connected by a string, they will have the same acceleration. That is, the net force divided by the mass for each object must be the same. Solving systems of equations If you have several unknown quantities that are related by a system of equations, it is necessary to have an equal number of unknowns and equations. Isolate one unknown quantity and substitute the expression into other equations to eliminate the unknown quantity. Repeat until one unknown value is known. Solving for the dynamics of a kinematics problem If a situation includes information about the motion of an object and you wish to solve for the forces acting on an object, the way to relate kinematics (position, velocity, acceleration) to dynamics (forces) is through Newton’s 2 nd law. The net force is proportional to the acceleration. Chapter Summary (Use the space below to summarize the chapter.) Sample Problems 1. What average force is required to bring a 1500 kg car to rest from a speed of 100km/h within a distance of 55m? 2. A box of mass 10kg is resting on the smooth (frictionless) horizontal surface of a table. (a) Determine the weight of the box and the normal force exerted on it by the table. (b) Now your frident pushes down on the box with a force of 40N. Again, determine the normal force exerted on the box by the table. (c) If your pull upward on the box with a force of 40n, what is the normal force? 3. Calculate the sum of the two forces exerted on the boat by the two workers? 4. Two boxes, A and B, are connected by a cord and rest on a smooth (frictionless) table. The boxes have masses of 12kg and 10kg. A horizontal force FP of 40N is applied to the 10kg box, as shown. Find the acceleration of each box and the tension in the cord connecting the boxes. 5. A mover is trying to lift a piano up to a second story apartment. He is using a rope looped over two pulleys as shown. What force must he exert on the rope to slowly lift the piano’s 2000N weight? 6. A 10kg box rests on a horizontal floor. The coefficient of static friction is 0.40 and the coefficient of kinetic friction is 0.30. Determine the force of friction acting on the box if a horizontal external applied force FA is exerted on it of magnitude (a) 0 (b) 10N (c) 20N, (d) 38N, and (E) 40 N. What is the acceleration of the box in each case? 7. Two boxes are connected by a cord running over a pulley. The coefficient of kinetic friction between box A and the table is 0.20. We ignore the mass of the cord and the pulley and any friction in the pulley, which means we can assume that a force applied to one end of the cord will have the same magnitude of the other end. We with to find the acceleration of the system which will have the same magnitude for both boxes assuming the cord doesn’t stretch. As box B moves down, box A moves to the right.