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Transcript
Questions to think about • Which object exerts the force • Why ramps make is easier to lift objects • Why is it heavier to ride a bicycle uphill placing a feather on an orbit F=m⋅a Puzzle: Is a person strong enough to accelerate an object into an orbit around the earth? Isn’t it just a matter of object’s mass? Answer: A light object does not allow a person to apply the required force! What is pulling what? F12 F21 Both object equally contribute to the interaction Newton’s third law of motion: For every force that one object exerts on the second object, there is an equal (in magnitude) but oppositely directed force that the second object exerts on the first object. Puzzle: Which pulls stronger (due to gravity): earth on you or you on earth? fiddler on the roof - support and friction static frictional force fs (exerted by the roof) support force N (exerted by the roof) - normal gravitational force W (exerted by the earth) 1. When two object are in contact along a rigid surface, they may exert a support force on each other. The force is perpendicular to the surface in contact and adjusts itself to the situation. 2. When two object are in contact along a rigid surface and do not slide, they may exert a static frictional force on each other. The force is parallel to the surface in contact and also adjusts its value. fiddler on a slippery roof kinetic frictional force static frictional force f s fk (exertedbybythe theroof) roof) (exerted support force N (exerted by the roof) net force gravitational force W (exerted by the earth) The magnitude of the static frictional force is restricted by fs ≤ µs ⋅ N When the object slides the kinetic frictional force has value fk = µk ⋅ N and is opposite to sliding direction. free body diagram includes • • • • Only forces exerted on the body. Only forces exerted by other bodies. All forces exerted on the body. Each force counted only once. missing force suction force exerted by nothing magic force of motion gravitational force exerted by earth net force for double count just to be sure: weight of the object force exerted by gravity How strong to push? When rolling along the ramp, the person applies a force much smaller (in magnitude) than the weight of the object. When lifting, the person applies a force equal (in magnitude) to the weight of the object. N1 S The ramp provides mechanical advantage N1 M.A. ≡ N2 N2 W W How to get a job done? The ability of a system to produce motion and structural rearrangements is called: E N E R G Y I have kinetic energy I have potential energy I have used the energy Keeping track of energy • • • • The total energy of an isolated system is conserved. Energy can be transferred from one object to another. There are two ways of energy transfer: work and heat. Energy of an object can change its form. Chemical (potential) energy of the food Gravitational potential energy of the piano Kinetic energy of the piano y the work 1cm -1cm -0.02 N dW = Fx ⋅ dx + Fy ⋅ dy + Fz ⋅ dz x dW = (- 0.02) N ⋅ (- 0.01) m = 0.1 mJ For a small displacement of an object, the scalar product of a force applied to the object due to a certain interaction and the displacement of a selected point of the object in the direction of the force is called t h e w o r k , done on the point of the object, due to the interaction. The work along a path of an object, is equal to the sum of work done along all small displacements constituting the path. The SI unit of work is the joule: 1J = 1 N ⋅ 1 m make a point of the point Fs>0 c.f. c.m. dy<0 Example 1 Determine the work done by the person on the “center of mass” of the yo-yo (together with the string), over a small displacement. dWc.m. = Fs⋅ dy < 0 J Example 2 Determine the work done by a person on the “center of the force” exerted on the yo-yo, over a small displacement. dWc.f. = 0 J May the Work be with you, too Work is a measure of cumulative interaction between objects. Fs W 1. 2. 3. 4. 5. Work is done (performed) on an object, on a specific point associated with the object, only by other objects. Work is done along a path of the object, and is always due to an interaction. Example. A person performed work due to friction on the center of mass of the yo-yo, as it moved from the hand to its lowest point. Example. The earth performed work due to gravity on the center of mass of the yo-yo, as it moved from the hand to its lowest point. Example. The earth performed work due to gravity on the center of gravity of the yo-yo, as it moved from the hand to its lowest point. potential energy For some interactions, the work does not depend on the path. These are called conservative interactions. Gravity is conservative ! 2 Only conservative interactions result in a potential energy. h 1 Work Wc done due a conservative interaction, along a any path between two locations of the object, is opposite to the change in potential energy along this path ∆ U = - Wc Gravitational Potential Energy (near the surface of a planet) Ug = m ⋅ g ⋅ h work on a ramp Change in gravitational potential energy: ∆Ug = - Wg = m ⋅ g ⋅ h Where to get the required energy from? The same effect is achieved: LARGE FORCE ⋅ small displacement = = small force ⋅ LARGE DISPLACEMENT The mechanical advantage: S N1 L = N2 h N1 lifting: W = N1⋅ h = ∆Ug on the ramp: W = N2⋅ L = ∆Ug N2 L h W W riding a bicycle (with constant velocity) Drag (air resistance) – a frictionlike interaction between a fluid and a solid object moving in fluid, resulting in slowing the relative motion. The force depends on the relative velocity of the object and the fluid S Fs S D Fs D W The energy remains constant (Wg = 0 J) Ws = - WD and Fs = D W The energy is increasing (Wg < 0 J) Ws > - WD and Fs > D