Transcript Work
Group Work Rank the following scenarios from least work done to most work done. A. 100 N 10 m 100 N D. B. 100 m 10 N 100 m 100 N C. E. 100 N 100 m 0m Work force is not all that matters § 6.1–6.2 What’s the point? Energy is critically important to Nature. Objectives • Relate work to force and distance. • Calculate the kinetic energy of a moving object. Work Formula W = work = F·s F = force applied s = displacement Units of Work joule (J) = 1 newton along 1 meter kg m kg m2 J = Nm = m = s2 s2 Group Work Estimate the work done by the strong man in the video. Justify your estimates of force and distance. Work is a Scalar component of force in direction of motion Source: Griffith, The Physics of Everyday Phenomena Dot Product of Vectors a f a·b = ab cos f a b b Commutative Dot Product Geometrically • Product of the projection of one vector onto the other • “Overlap” a ab cos f f b Dot Product by Components If A = Axi + Ayj + Azk B = Bxi + Byj + Bzk then A·B = AxBx + AyBy + AzBz Dot Product Properties • Positive if |f| < p/2 • Negative if |f| > p/2 – + • Zero if vectors perpendicular (|f| = p/2) • Maximum magnitude if parallel or antiparallel Think Question The piglet has a choice of three frictionless slides to descend. Along which slide is the greatest net force exerted on the piglet? A B C D. The net force is the same for all. Think Question The piglet has a choice of three frictionless slides to descend. Along which slide would the piglet slide the longest distance? A B C D. The distance is the same for all. Think Question The piglet has a choice of three frictionless slides to descend. Along which slide would the piglet finish soonest? A B C D. The time is the same for all. Poll Question The piglet has a choice of three frictionless slides to descend. Along which slide would gravity do the most work on the piglet? A D. Same work for all. B C E. Need more information. Example Problem A luggage handler at the Laramie Airport pulls a 20-kg suitcase from rest up a ramp inclined at 25° above the horizontal with a force of 140 N parallel to the ramp. The coefficient of kinetic friction between the ramp and the box is mk = 0.30. The suitcase travels 3.80 m along the ramp. Find a. the work done on the suitcase by the handler b. the work done on the suitcase by gravity c. the work done on the suitcase by the normal force d. the work done on the suitcase by friction e. the total work done on the suitcase f. the final speed of the suitcase Total (Net) Work If several forces act on a moving object: s F4 F1 F2 • W = (SF)·s or • W = S(F·s) F3 Poll Question To accelerate an object from 10 to 20 m/s requires A. more work than to accelerate from 0 to 10 m/s. B. the same amount of work as to accelerate from 0 to 10 m/s. C. less work than to accelerate from 0 to 10 m/s. Work of Acceleration • To accelerate to speed v with constant force F slope = a = v F = m t v area = Dd speed time • Work = F·Dd t mv 1 Dd = 2 vt F = m (slope) = t mv 1 1 2 mv vt = • Work = 2 2 t Another Perspective • So, for the 0–10 vs. 10–20 m/s case: • If same force, then same time – a’s and Dv’s are equal, so Dt’s are equal • Average speeds are 5 vs. 15 m/s • The 10–20 m/s case travels 3 as far A Moving Object Can Do Work Source: Griffith, The Physics of Everyday Phenomena Kinetic Energy the work to bring a motionless object to speed K= 1 2 mv2 equivalent to the work a moving object does in stopping Think Question Which has more kinetic energy? A. 10 kg 10 m/s 5 kg 10 m/s 5 kg 40 m/s 10 kg 20 m/s B. C. D. Poll Question The piglet has a choice of three frictionless slides to descend. Along which slide would the piglet finish with the highest speed? A B C D. The final speed is the same for all. Work-Energy Theorem • If an amount of net work w is done on an otherwise isolated system, the system’s kinetic energy changes by an amount DK = w.