* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 4, Part III
Survey
Document related concepts
Jerk (physics) wikipedia , lookup
Classical mechanics wikipedia , lookup
Fictitious force wikipedia , lookup
Equations of motion wikipedia , lookup
Mass versus weight wikipedia , lookup
N-body problem wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Centripetal force wikipedia , lookup
Transcript
Applications & Examples of Newton’s 2nd Law Example 4-11 A box of mass m = 10 kg is pulled by an attached cord along a horizontal smooth (frictionless!) surface of a table. The force exerted is FP = 40.0 N at a 30.0° angle as shown. Calculate: a. The acceleration of the box. b. The magnitude of the upward normal force FN exerted by the table on the box. Free Body Diagram The normal force, FN is NOT always equal & opposite to the weight!! Example 4-12 Two boxes are connected by a lightweight (massless!) cord & are resting on a smooth (frictionless!) table. The masses are mA = 10 kg & mB = 12 kg. A horizontal force FP = 40 N is applied to mA. Calculate: a. Acceleration of the boxes. b. Tension in the cord connecting the boxes. Free Body Diagrams Example 4-13 (“Atwood’s Machine”) Two masses suspended over a (massless frictionless) pulley by a flexible (massless) cable is an “Atwood’s machine” . Example: elevator & counterweight. Figure: Counterweight mC = 1000 kg. Elevator mE = 1150 kg. Calculate a. The elevator’s acceleration. b. The tension in the cable. a a aE = - a Free Body Diagrams aC = a Conceptual Example 4-14 Advantage of a Pulley A mover is trying to lift a piano (slowly) up to a second-story apartment. He uses a rope looped over 2 pulleys. What force must he exert on the rope to slowly lift the piano’s mg = 2000-N weight? mg = 2000 N Free Body Diagram Example 4-15 = 300 N Newton’s 3rd Law FBR = -FRB, FCR = -FRC FRBx = -FRBcosθ FRBy = -FRBsinθ FRCx = FRCcosθ FRCy = -FRCsinθ Example: Accelerometer A small mass m hangs from a thin string & can swing like a pendulum. You attach it above the window of your car as shown. What angle does the string make a. When the car accelerates at a constant a = 1.20 m/s2. b. When the car moves at constant velocity, v = 90 km/h? Free Body Diagram General Approach to Problem Solving 1. Read the problem carefully; then read it again. 2. Draw a sketch, then a free-body diagram. 3. Choose a convenient coordinate system. 4. List the known & unknown quantities; find relationships between the knowns & the unknowns. 5. Estimate the answer. 6. Solve the problem without putting in any numbers (algebraically); once you are satisfied, put the numbers in. 7. Keep track of dimensions. 8. Make sure your answer is REASONABLE! Problem 25 FT1 a m1g FT2 Take up as positive. FT2 a m2g Newton’s 2nd Law ∑F = ma (y direction) for EACH bucket separately!!! m1 = m2 = 3.2 kg m1g = m2g = 31.4 N Bucket 1: FT1 - FT2 - m1g = m1a Bucket 2: FT2 - m2g = m2a Problem 29 Take up as positive. Newton’s 2nd Law: ∑F = ma (y direction) on woman + bucket! FT m = 65 kg, mg = 637 N FT FP a a mg FT + FT - mg = ma 2FT - mg = ma Also, Newton’s 3rd Law: FP = - FT