2/6/14 Agenda Chapter 3, Problem 28 • Today: Homework Quiz, Chapter 4 A ball with a horizontal speed of 1.25 m/s (Newton’s Laws) rolls off a bench 1.00 m above the floor. • Thursday: Applying Newton’s Laws • Start reading Chapter 5 a. How long will it take the ball to hit the floor? b. How far from a point on the floor directly below the edge of the bench will the ball land? Forces Contact and Field Forces • Usually think of a force as a push or pull • Vector quantity • May be a contact force or a field force – Contact forces result from physical contact between two objects – Field forces act between disconnected objects • Key idea: Forces act on objects and change their motion. Fundamental Forces External and Internal Forces • Types • External force – Strong nuclear force – Any force that results from the interaction – Electromagnetic force between the object and its environment – Weak nuclear force • Internal forces – Gravity – Forces that originate within the object itself • Characteristics – They cannot change the object’s velocity – All field forces – Listed in order of decreasing strength – Only gravity and electromagnetic in mechanics 1 2/6/14 Inertia vs. Mass Newton’s First Law • Inertia is the tendency of an object to • An object moves with a velocity that is continue in its original motion constant in magnitude and direction, • Mass is a measure of the resistance of an unless acted on by a nonzero net force object to changes in its motion due to a – The net force is defined as the vector sum of force all the external forces exerted on the object – Scalar quantity – SI units are kg Newton’s Second Law Gravitational Force • The acceleration of an object is directly • Mutual force of attraction between any two proportional to the net force acting on it, and objects inversely proportional to its mass. • Expressed by Newton’s Law of Universal ∑F Gravitation (more later): a = or F = ma m ∑ m m – F and a are both vectors F = G 1 2 g r 2 • Can also be written in component-form • Force unit: the newton (1 N = 1 kg m/s2) Weight More about weight • The magnitude of the gravitational force • Weight is not an inherent property of an acting on an object of mass m near the object Earth’s surface is called the weight w of – mass is an inherent property the object – w = m g is a special case of Newton’s Second • Weight depends upon location Law – g is the acceleration due to gravity 2 2/6/14 Newton’s Third Law Newton’s Third Law cont. • If object 1 and object 2 interact, the force • F12 may be called exerted by object 1 on object 2 is equal in the action force and magnitude but opposite in direction to the F21 the reaction force exerted by object 2 on object 1. force – F F – Actually, either force 12 = − 21 can be the action or the reaction force – This is like saying a single isolated force • The action and cannot exist in a system reaction forces ALWAYS act on DIFFERENT objects Discussion: The stubborn donkey Agenda A very lazy donkey is hitched to a cart, but • Today: Solving Newton’s Laws problems refuses to move. He says: “because of • Tuesday: More examples (Chapter 5) Newton’s third law, if I pull on the cart then • Heads-up: First exam is a week from the cart will pull on me with a force that is Tuesday. equal in strength & opposite in direction. So • Homework #4 Due next week (the first I will never be able to pull the cart.” exam will cover HW 1-4) How would you convince the donkey that he’s wrong? Applications of Newton’s Laws Free Body Diagrams • Assume: • Must identify all the forces acting on the – Objects behave as particles object of interest • can ignore rotational motion (for now) • Choose an appropriate coordinate system – Masses of strings or ropes are negligible • If the free body diagram is incorrect, the – Interested only in the forces acting on the solution will likely be incorrect object • can neglect reaction forces 3 2/6/14 Solving Newton’s Second Law Free Body Diagrams Problems • Read the problem at least once • The force is the tension acting on the box • Draw a picture of the system – The tension is the same at – Identify the object of primary interest all points along the rope – Indicate forces with arrows n and F • g are the forces exerted by the ground • Label each force and the Earth’s gravity – Use labels that bring to mind the physical quantity involved Solving Newton’s Second Law Equilibrium Problems • Draw a free body diagram • An object either at rest or moving with a – If additional objects are involved, draw constant velocity is said to be in separate free body diagrams for each object equilibrium – Choose a convenient coordinate system for each object • The net force acting on the object is zero • Apply Newton’s Second Law (since the acceleration is zero) – The x- and y-components should be taken from the vector equation and written separately F = 0 • Solve for the unknown(s) ∑ Equilibrium Example – Free Body Equilibrium Diagrams • Easier to work with the equation in terms of its components: FandF00 ∑∑xy== 4 2/6/14 Inclined Planes Multiple Objects – Example • When you have more than one object, the • Choose the problem-solving strategy is applied to each coordinate object system with x along the incline • Draw free body diagrams for each object and y • Apply Newton’s Laws to each object perpendicular to • Solve the equations the incline • Replace the force of gravity with its components Multiple Objects – Example, cont. Forces of Friction • When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion – This is due to the interactions between the object and its environment • This is resistance is called friction More About Friction Static Friction, ƒs • Friction is proportional to the normal force • The force of static friction is generally greater • Static friction acts to keep than the force of kinetic friction the object from moving • The coefficient of friction (µ) depends on the surfaces in contact • If F increases, so does ƒs • The direction of the frictional force is opposite • If F decreases, so does ƒs the direction of motion • ƒ ≤ µ N • The coefficients of friction are nearly s independent of the area of contact 5 2/6/14 Forces Lecture-Tutorial Kinetic Friction, ƒk • Work with a partner or two • The force of kinetic friction • Read directions and answer all questions acts when the object is in carefully. Take time to understand it now! motion • Come to a consensus answer you all • ƒk = µ N agree on before moving on to the next – Variations of the coefficient question. with speed will be ignored • If you get stuck, ask another group for help. • If you get really stuck, raise your hand and I will come around. Block on a Ramp, Example Connected Objects • Axes are rotated as usual on an incline • Apply Newton’s Laws separately to each object • The direction of impending motion • The magnitude of the would be down the acceleration of both plane objects will be the same • Friction acts up the • The tension is the same in plane each diagram – Opposes the motion • Solve the simultaneous • Apply Newton’s equations Laws and solve equations 6 .