Announcements Test 1 next Thursday, 5–7 PM Covers material in Chapters 2–5 Review session –Monday 5:30–7 PM, CR 103 –Bring your questions

Group Work 1.Rank the following scenarios from least work done to most work done. 10 m 100 N A. 100 m 10 N B. 100 m 100 N C. 100 N 100 m D. 100 N 0 m E.

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.

CPS Question Work is A.Force  time. B.Force  distance C.Force / distance. D.Force / time. E.Mass  velocity

Work Formula W = work = F·s F = force applied s = displacement

Units of Work J = Nm = kg m m = s2s2 kg m 2 s2s2 joule (J) = 1 newton along 1 meter

Group Work 2.Estimate the work done by the strong man in the video. Show your work! Justify your estimates of force and distance.

Work is a Scalar Source: Griffith, The Physics of Everyday Phenomena component of force in direction of motion

Dot Product of Vectors a·b = ab cos  a b a b  Commutative

Dot Product Geometrically Product of the projection of one vector onto the other “Overlap” b cos  a cos  a b  ab cos 

Dot Product by Components If then A·B = A x B x + A y B y + A z B z A = A x i + A y j + A z k B = B x i + B y j + B z k

Dot Product Properties Positive if |  | <  /2 Negative if |  | >  /2 Zero if vectors perpendicular (|  | =  /2) Maximum magnitude if parallel or anti- parallel + –

CPS Question The piglet has a choice of three frictionless slides to descend. Along which slide is the greatest net force exerted on the piglet? ABC D.The net force is the same for all.

CPS Question The piglet has a choice of three frictionless slides to descend. Along which slide would the piglet slide the longest distance? ABC D.The distance is the same for all.

CPS Question The piglet has a choice of three frictionless slides to descend. Along which slide would the piglet finish soonest? ABC D.The time is the same for all.

Group CPS Question The piglet has a choice of three frictionless slides to descend. Along which slide would gravity do the most work on the piglet? ABC D. Same work for all.E. Need more information.

Group Work Problem 4 on the worksheet –use sum of products of components

s Total (Net) Work If several forces act on a moving object: F1F1 F2F2 F3F3 F4F4 or W = (  F)·s W =  (F·s)

Example Problem 6.57 A luggage handler at the Laramie Airport pulls a 20-kg suitcase 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  k = 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, if its initial speed was zero

CPS 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 t v speed time mv t F = m (slope) = 1 2  d = vt Work = F·  d Work = = mv vt 1 2 mv t slope = a = F m v t = area =  d

Another Perspective So, for the 0–10 vs. 10–20 m/s case: If same force, then same time –a’s and  v’s are equal, so  t’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 KE = 1 2 mv 2 equivalent to the work a moving object does in stopping

Which has more kinetic energy? A. B. C. D. 10 kg10 m/s 5 kg10 m/s 10 kg20 m/s 40 m/s5 kg CPS Question

The piglet has a choice of three frictionless slides to descend. Along which slide would the piglet finish with the highest speed? ABC D.The final speed is the same for all.

Work-Energy Theorem If an amount of work w is done on an otherwise isolated system, the system’s energy changes by an amount  E = w.