L40 Work - L40{ Work Work w : product of force and distance...

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L40{ Work Work w : product of force and distance moved Let f ( x ) be the force acting on an object at each point x in [ a;b ]. Then the work , w , needed to move the object from x = a to x = b is: w = lim n !1 n X i =1 f ( x i x w = R b a f ( x ) dx To calculate work of a non-constant force, you inte- grate over the force function. Unit : f ( x ) in newtons, d in meters, ! W in joule( J )). f ( x ) in pounds, d in feet, ! W in foot-pound. We will calculate work problems ±±± 1. related to Hook’s Law, Spring Problems 2. of a cable/rope problem 3. required to Drain a Tank 1
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Finding Work in conjunction with Hooke’s Law Hooke’s Law states that the force required to hold a spring stretched 0 x 0 units beyond its natural length is proportional to the amount/distance x stretched: f ( x ) = kx ( k = spring constant) ex. A force of 10 lb is required to hold a spring stretched 4in beyond its natural length. How much work is done in stretching it from its natural length to 6in beyond its natural length? (Use foot-pounds!) Want to calculate: Given: 2
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L40 Work - L40{ Work Work w : product of force and distance...

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