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 and Energy

What’s the point? Energy is critically important to Nature.

Objectives Relate work to force and distance. Calculate an object’s gravitational potential energy near the earth’s surface. Calculate the kinetic energy of a moving object.

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

Work Formula work = F·  d F = force applied  d = distance traveled

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

Can You See Why The work required to lift a mass m a height h above the earth’s surface is w = mgh Hint: What is the force applied? What is the distance traveled?

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

Potential Energy The energy of relative position of two objects gravity springs electric charges chemical bonds = the work you can get from the force.

Gravitational Potential Energy Gravitational potential energy = the work to raise an object to a height Gravitational PE = mgh = the work gravity does lowering the object

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 Properties Maximum if vectors in same direction Negative if vectors in opposite directions Zero if vectors perpendicular

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

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

Group 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? ABC D. Same work for all.E. Need more information.

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.

It Takes Work Source: Griffith, The Physics of Everyday Phenomena to speed something up.

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

Kinetic Energy the work to bring a motionless object to speed K = 1 2 mv 2

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 Poll Question

Work-Energy Theorem If net work W is done on a system, the system’s kinetic energy changes by  K = W.

Horse Handling Bitey end Kicky end Stompy parts

Dangerous View

Minimize Kinetic Energy minimize possible  d

Reading for Next Time Conservation of energy Big ideas: –The total amount of energy is invariant –Energy can change form