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Conceptual Example A stone mason drags a marble block across a floor by pulling on a rope attached to the block. The block may or may not be in equilibrium. How are the various forces related? What are the action-reaction pairs? B R M – Typeset by FoilTEX – 1 Clicker Question A weight lifter struggles but manages to keep a heavy barbell above his head. Occasionally he slips and the barbell starts to fall downward, but he always recovers. Compare the force exerted by the weight lifter on the barbell to that exerted by the barbell on the weight lifter. During the slip when the barbell starts to fall downward, the force exerted by the weight lifter on the barbell is A. less than B. greater than C. the same as the force the barbell exerts on the weight lifter. – Typeset by FoilTEX – 2 Newton’s 1st & 2nd Laws: General Strategy • Identify relevant concepts P~ P~ – F = m~a or F = 0 (equilibrium) – target variables & known variables • Set-up – – – – – DRAW A PICTURE! DRAW A FREE BODY DIAGRAM Label all forces with a symbol for magnitude Choose coordinate system and draw axes. If more than one body, write relationships between 2 bodies – Typeset by FoilTEX – 3 Newton’s 1st & 2nd Laws: General Strategy (con’t) • Evaluate – Determine components of each force along coordinate axes – For each object, write an equation for each component of Newton’s 2nd law – List knowns & unknowns & target variables – Check that number of equations matches number of unknowns – Solve equations (without plugging in numbers) • Assess – Check units – Does answer make sense? – Typeset by FoilTEX – 4 Hooke’s Law Springs are often used to measure forces since the stretch or compress in response to the applied force. For an ideal spring, the stretch or compression is directly proportional to the force: Fspring = −kx where x is the amount of stretch/compression, and k is the spring constant. – Typeset by FoilTEX – 5 Example 4.5 A helicopter rises vertically, carrying a load of concrete for the foundation of a ski lift. A 35 kg bag of concrete sits in the helicopter on a spring scale whose spring constant is 3.4 kN/m. By how much does the spring compress a. when the helicopter is at rest? b. when it’s accelerating upward at 1.9 m/s2? – Typeset by FoilTEX – 6 Example A light rope is attached to a block with mass 4.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is 10.0 N. A. Draw 2 free body diagrams, one for the 4.00 kg block and one for the block with mass m. B. What is the acceleration of either block? C. What is the mass m of the hanging block? D. How does the tension compare to the weight of the hanging block? – Typeset by FoilTEX – 7 Frictional forces – Typeset by FoilTEX – 8 Frictional forces • friction always opposes direction of motion • frictional force is always parallel to surface • frictional force is always perpendicular to the normal force – Typeset by FoilTEX – 9