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Chapter 4 Dynamics: Forces Notes Anything in red is extra examples and information necessary for understanding concepts, but not necessary to write 4-1 Force A force is a push or pull. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity. Force is a vector. Measured in Newtons (N) 1 N = 1 kgm/s2 Forces are always at work, even on stationary objects. • Fields existing in space can be used to explain all interactions • Forces are interactions between objects that don’t actually touch • All forces are determined by the 3 fundamental forces – Gravitational – Electroweak (formerly electromagnetic and nuclear weak) – essentially forces existing between charges – Strong – force that holds a nucleus together • Forces act through “contact” or at a distance. • Contact force: result from actual physical contact with objects (no real such thing - electroweak) • Examples? • Field force or long-range: no contact occurs but the force exists • Examples? • Forces associated with solids – Normal (N, Fn) The force between two solids in contact that prevents them from occupying the same space. The normal force is directed perpendicular to the surface. A "normal" in mathematics is a line perpendicular to a planar curve or surface; thus the name "normal force". – Friction (ƒ, Fƒ) The force between solids in contact that resists their sliding across one another. Friction is directed opposite the direction of relative motion or the intended direction of motion of either of the surfaces. – Tension (T, Ft) The force exerted by an Tension object being pulled upon from opposite ends like a string, rope, Tension cable, chain, etc. Tension is directed along the axis of the object. – Elasticity (Fe, Fs) The force exerted by an object under deformation (typically tension or compression) that will return to its original shape when released like a spring or rubber band. Elasticity, like tension, is directed along an axis (although there are exceptions to this rule). – Centripetal – a net force that makes an object travel in a circular or curved path (typically due to tension from a central axis) • Forces associated with fluids. Fluids include liquids (like water) and gases (like air). – Buoyancy (B, Fb) The force exerted on an object immersed in a fluid. Buoyancy is usually directed up (although there are exceptions to this rule). – Drag (R, D, Fd) Friction in a fluid. – Lift (L, Fl) The force that a moving fluid exerts as it flows around an object; typically a wing or wing-like structure, but also golf balls and baseballs. Lift is generally directed perpendicular to the direction of fluid flow (although there are exceptions to this rule). – Thrust (T, Ft) The force that a fluid exerts when expelled by a propeller, turbine, rocket, squid, clam, etc. Thrust is directed opposite the direction the fluid is expelled. • Forces associated with physical phenomena. – Gravity or Weight (Fg, W) – Electrostatic Force (FE) The attraction or repulsion between charged bodies. Experienced in everyday life through static cling and as the explanation behind much of basic chemistry. – Magnetic Force (FB) The attraction or repulsion between charged bodies in motion. Experienced in everyday life through magnets and as the explanation behind why a compass needle points north. • Fictitious forces. Apparent forces objects experience in an accelerating coordinate system (i.e. accelerating car, airplane, spaceship, elevator, rides). Fictitious forces are a consequence of trying to keep up with an accelerating environment and are not exerted by another object like real forces. – Centrifugal Force The force experienced by all objects in a rotating coordinate system that seems to pull them away from the center of rotation. – Coriolis Force The force experienced by moving objects in a rotating coordinate system that seems to deflect them at right angles to their direction of motion. – "G Force" Not really a fictitious force but rather gravity-like sensation experienced by objects in an accelerating coordinate system. Wind direction Wind flows into area of low pressure and deflected to the right in N. Hemisphere – counterclockwise rotation of hurricanes • Force Diagram: shows all forces (as vectors) acting in a situation. N • Free Body Diagram: shows the forces (as vectors) that act on one object of interest. Net force • The net force is the sum of all the forces • Equilibrium: ∑F = 0 – Static equilibrium vs. Dynamic equilibrium • Objects will accelerate in the direction of a nonzero net force • Finding net force: resolve all forces into vector components and add the vectors as normal 4-7 Solving Problems with Newton’s Laws— Diagrams 1. Draw a sketch. 2. For one object, draw a free-body diagram, showing all the forces acting on the object. Make the magnitudes and directions as accurate as you can. Label each force. If there are multiple objects, draw a separate diagram for each. © 2014 Pearson Education, Inc. Free-Body Newton’s Laws Notes Anything in red is extra examples and information necessary for understanding concepts, but not necessary to write 18 Nov. Newton’s First Law of Motion The law of inertia. Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it. Inertial reference frames: • An inertial reference frame is one in which Newton’s first law is valid. • Rotating and accelerating frames are NOT inertial. • Relativity Principle: the basic laws of physics are the same in all inertial reference frames, no one reference frame is better than another when viewed from train when viewed from ground • Fictitious forces appear in accelerating reference frames. • Example: Earth is rotating, so not inertial • Example: An accelerating elevator • Example: An accelerating car The Theory of Relativity • Special theory of relativity – inertial reference frames – Relativity principle - there is no way for an observer to determine if a given reference frame is at rest or moving at constant velocity in a straight line • General theory of relativity – accelerating reference frames and gravity – Equivalence principle – no observer can determine by experiment whether he or she is accelerating or in a gravitational field Conceptual Practice Problems 1. An astronaut is always tethered to the space shuttle when outside of the shuttle. Why? 2. A school bus comes to a sudden stop, and all of the backpacks on the floor start to slide forward. What force causes them to do that? Explain the situation and draw a free-body diagram. Newton’s Second Law of Motion Acceleration is proportional to force and inversely proportional to mass. *slightly different on equation sheet Inertial Mass Mass is the measure of inertia of an object. In the SI system, mass is measured in kilograms. Mass is not weight: • Mass is a property of an object. Weight is the force exerted on that object by gravity. Weight = mass x gravity • Pounds are a unit of Force, not mass • If you go to the moon, whose gravitational acceleration is about 1/6 g, you will weigh much less. Your mass will be the same. • Gravitational mass = when one body attracts another (universal law of gravitation) Weight and Normal Force Weight is the force exerted on an object by gravity. Close to the surface of the Earth, where the gravitational force is nearly constant, the weight is: The force exerted perpendicular to a surface is called the normal force. It is exactly as large as needed to balance the force from the object (if the required force gets too big, something breaks!) (4-3) Newton’s Third Law of Motion • Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first. • The forces are acting on DIFFERENT objects Solving Problems with Newton’s Laws 1. Draw a sketch and/or freebody diagram, showing all the forces acting on the object. Make the magnitudes and directions as accurate as you can. Label each force. If there are multiple objects, draw a separate diagram for each. 3. Resolve vectors into components. 4. Apply Newton’s second law to each component. 5. Solve. Practice Problems 4-3. What net force is required to bring a 1500kg car to rest from a speed of 100km/h (28m/s) within a distance of 55m? 4-6. A 10.0kg box is resting on a frictionless horizontal surface. A) Determine the weight and normal force. B)Your friend pushes down on it with a force of 40.0N. Again determine the weight and normal force. C) If your friend now pulls up with a force of 40.0N, what is the normal force? 4-7. What happens when a person pulls upward with a force of 100.0N on a 10.0kg box? 4-11. Now your friend pulls on the 10.0kg box with a force of 40.0N but at an angle of 30.0°. Calculate the a) Acceleration of the box, and b) the normal force (ignore friction). 4-12. Two boxes are connected by a lightweight cord and are resting on a table. The boxes have masses of 12.0kg and 10.0kg. A horizontal FP of 40.0N is applied by a person to the 10.0kg box. Find the a) acceleration of each box and b)tension in the cord between the two boxes. 4-13. Masses suspended over pulleys are known as an Atwood’s Machine . Consider an elevator (m1=850kg) and its counterweight (m2=1000kg). When 4 passengers are in the elevator m1=1150kg. Calculate the acceleration of the elevator with the passengers and the tension in the cable. Finding her car stuck in the mud, a bright physics student ties a strong rope to the back bumper of the car and the other end to a tree. She pushes the midpoint of the rope with her maximum effort which she estimates to be Fp=300N. The car just begins to budge with the rope at an angle θ which she estimates to be 5°. With war force is the rope pulling on the car? Neglect the mass of the rope. Chapter 4 4 Dec. Dynamics: Friction and Inclined Plane Notes Assignment 2: • Misconception questions • Q9,10,20 • P9,12,17,20,21,24, 25,46,49 Kinetic Friction Kinetic—sliding—friction: μk is the coefficient of kinetic friction, and is different for every pair of surfaces. *slightly different on equation sheet This table lists the measured values of some coefficients of friction. Note that the coefficient depends on both surfaces. © 2014 Pearson Education, Inc. Static friction is the frictional force between two surfaces that are not moving along each other. Static friction keeps objects on inclines from sliding, and keeps objects from moving when a force is first applied. *slightly different on equation sheet The static frictional force increases as the applied force increases, until it reaches its maximum. Then the object starts to move, and the kinetic frictional force takes over. Inclined Planes An object sliding down an incline has three forces acting on it: the normal force, gravity, and the frictional force. • The normal force is always perpendicular to the surface. • The friction force is parallel to it. • The gravitational force points down. If the object is at rest, the forces are the same except that we use the static frictional force, and the sum of the forces is zero. Practice Problems 4-16. A 10.0kg box rests on a horizontal floor. The coefficient of static friction is µs = 0.40 and the coefficient of kinetic friction is µk = 0.30. Determine the force of friction Ff, acting on the box if a horizontal external applied for of FA is exerted on it of magnitude a) 0N, b)10N, c)20N, d)38N, and e)40N. Under which applied force(s) does the box accelerate and by how much? 4-19. Your little sister wants a ride on her sled. If you are on flat ground, will you exert less force if you push her or pull her? Assume the same angle in each case. Explain. 4-20. Two boxes are connected by a cord running over a pulley. The µk = between box I and the table is 0.20. Find acceleration of the system which will have the same magnitude for both boxes assuming the cord doesn’t stretch. As box II moves down, box I moves to the right. 5.0kg 2.0kg 4-21. A skier has just begun descending a 30 degree slope. Assuming the µk = 0.10, a) draw a free body diagram, then b) calculate her acceleration and c) the speed she will reach after 4.0s.