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Forces & Newton's Laws PHYSICS 1 Forces & Newton’s Laws Advanced Placement Presenter 2014-2015 Forces & Newton’s Laws What I Absolutely Have to Know to Survive the AP* Exam Force is any push or pull. It is a vector. Newton’s Second Law is the workhorse of the AP Physics 1 exam. It allows you to write down mathematical relationships that are true. Thus, for a single body, if you pick any direction and sum up all the positive and negative forces that act on the body along that line, the sum will equal the product of the body’s mass and its acceleration along that line. A Free Body Diagram allows you to identify all of the forces acting on a single body. Neglect one force or add a fictitious force on your FBD and you are in trouble. • Newton’s 1st Law: in an inertial frame of reference, an object in a state of constant velocity (including zero velocity) will continue in that state unless impinged upon by a net external force. If ΣF=0, then a=0 and the object is at rest or moving at a constant velocity in a straight line. The converse is true also, if an object is in a state of constant velocity (including zero velocity) then a=0 and ΣF=0. • Newton’s 2nd Law: A net force acting on a mass causes that mass to accelerate in the direction of the net force. The acceleration (vector) is directly proportional to the net force (vector) acting on the mass and ΣF inversely proportional to the mass of the object being accelerated. a= or ΣFma= m • Newton’s 3rd Law: For every action force, there exists an equal and opposite reaction force. When one object exerts a force on a second object, the second object always responds with a duplicate force in the opposite direction. If you hit a table with your fist, then the size and direction of the force you apply must be equal and opposite the force the table applies to you. Forces are generated in action/reaction pairs that occur on different objects. If you try to apply 800 Newtons of force to a table that can only provide 600 Newtons of reaction force back on you, you will never succeed. The table will break as soon as you exceed 600 Newtons, which is the maximum force it can apply to you. Key Formulas and Relationships ΣFF=net =m a FmgW = FFstaticfsmax ≤ µ s N () FFkineticfk= µ k N () Gm m F = 12 G r2 kgm ΣF = Sum of the forces is the Net Force Newtons (N) = s2 a = acceleration m = mass FW = weight g = acceleration due to gravity Ffsmax = maximum static frictional force Ffk = kinetic frictional force FN = normal force FG = gravitational force r = distance between the centers of two masses AP* is a trademark of the College Entrance Examination Board. The College Entrance Examination Board was not involved in the production of this material. Copyright © 2013 National Math + Science Initiative®, Inc., Dallas, TX. All rights reserved. Forces & Newton’s Laws Basic Kinds of Forces Fg = mg Weight Fg , W Always directed toward the Earth’s center. Force on a free falling body, if we neglect air friction. mm FG= 12 G r 2 Gravitational F A force of attraction between any two massive objects. G When the Earth is one of the two bodies involved, then the force felt by the second body while positioned on the Earth’s surface will always be directed toward the Earth’s center. A force of support, provided to an object by a surface in which the object is in contact. Always directed perpendicular to and away from the surface providing the support. FN W In the figure above, a box isN supported by a table. The figure shows all the forces acting on the box and is called a Free Body Diagram (FBD). If a box, rests on a level table, then the FWmgN == . Notice that the normal force sometimes equals the weight but not always. Normal FN , N FN y mgsinθ x mgcosθ θ W If the box is placed on an inclined plane, then the FmgN = cosθ , the component of the weight that is equal and opposite the normal force. For the inclined plane above, the normal force and the weight are not equal and not even in the same direction. Copyright © 2013 National Math + Science Initiative®, Inc., Dallas, TX. All rights reserved Forces & Newton’s Laws Friction is produced by the atomic interaction between two bodies as they either slide over one another (kinetic friction) or sit motionless in contact with one another (static friction). FFfsmax ≤ µ s N (static) Static Friction opposes the intended direction of relative sliding. The static frictional force will only be as high as it needs to be to keep the system in equilibrium. If successively greater and greater forces are applied, the static frictional force will counter each push with a force of equal and opposite magnitude until the applied force is great enough to shear the bonding between the two surfaces. When you calculate fs or Ffsusing the equation above, you are finding the maximum static frictional force, one of an infinite number of possible frictional forces that could be exerted between the two bodies. µs is a proportionality constant called the coefficient of static friction. It is the ratio of the static frictional force between the surfaces divided by the normal force acting on the surface. FFfk= µ k N (kinetic) Kinetic Friction or Dynamic Friction or Sliding Friction is always Friction Ff , f opposite the direction of motion. The statement that kinetic friction is a function of the normal force only (surface area is independent) is true only when dealing with rigid bodies that are sliding relative to each other. When you calculate fk or Ff using the equation above, you are finding the single, constant kinetic frictional force that exists between the two bodies sliding relative to one another. No matter their velocity (assuming heating does not alter the coefficient of kinetic friction) the kinetic frictional force will always be the same. µk is a proportionality constant called the coefficient of kinetic friction. It is the ratio of the kinetic frictional force between the surfaces divided by the normal force acting on the surface WARNING! The two quantities fs and fk may look the same, but they tell us different things. Kinetic friction is typically less than static friction for the same two surfaces in contact. Note that the normal force sometimes equals the weight but not always. When you draw a free body diagram of forces acting on an object or system of objects, be sure to include the frictional force as opposing the relative motion (or potential for relative motion) of the two surfaces in contact. Copyright © 2013 National Math + Science Initiative®, Inc., Dallas, TX. All rights reserved Forces & Newton’s Laws FT is a force that is applied to a body by a rope, string, or cable. FT is applied along the line of the string and away from the body in Tension FT , T question. Push me, pull you force that does not fall into one of the above categories, for example, a friend shoves you. The magnitude of the applied force is characterized by an F, with any subscript that makes Applied F Subscript sense to solve the problem. Later in the year, you will encounter additional forces, like the electric force, FE, and the magnetic force, FB. Strategy on Force Problems 1. Take one body in the system and draw a Free Body Diagram (FBD) for it. 2. Choose x and y axes and place them beside your FBD. One axis must be in the direction of the acceleration you are trying to find. If there is no acceleration, then ΣF =0. 3. If there are forces on the FBD that are not along the x and y directions, find their respective x and y components. nd 4. Using Newton’s 2 Law, sum the forces in the x direction and set them equal to max . If a second equation is needed, sum the forces in the y direction and set them equal to may . 5. Repeat the above process for all the bodies in the system or until you have the same number of equations as unknowns and solve the problem. Effective Problem Solving Strategies A Free Body Diagram is normally depicted as a box showing all the forces acting on the body. These forces are depicted as arrows. They don’t have to be drawn to scale, but they should have a length that is appropriate for their magnitude. Also, the force vectors do need to be directionally accurate and Free Body Diagram labeled. Do not include components of the force vectors on your FBD. (FBD) When drawing Free Body Diagrams show only the force(s) that act on the body in question and do not show forces that the body applies to other bodies. Also, do not include velocity or acceleration vectors on your free body force diagrams, since you will lose points for extraneous vectors on your FBD. Copyright © 2013 National Math + Science Initiative®, Inc., Dallas, TX. All rights reserved Forces & Newton’s Laws Example 1 A rope supports an empty bucket of mass 3.0 kg. Determine the tension in the rope when the bucket is (a) at rest and (b) the bucket is accelerated upward at 2.0 m/s2. Solution Step 1 Draw a Free Body Diagram for each body in the system. FT W Step 2 Choose x and y axes.
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