A person is pulling a crate with a force of 50N as shown over a distance of 3 m. What is the work done on the object by the person? J 2.25 J 3.75 J J 60º 50N 3.0 m J J J J CLICKER! W = Fcos  s = 50 cos 60 x 3 = 75 J

A person is pulling a crate with a force of 50N as shown for 10s at a constant speed of 1.0 m/s. What is the work done on the object by the person? J 2.75 J 3.75 J J 60º 50N 3.0 m 1.0 m/s J J J J CLICKER! v =  x/t  x = vt = 1 m/s x 10s = 10 m W = Fcos  s = 50 cos 60 x 10 = 250 J

An object is pushed around by applying 50 N force in a circular path of radius 2m. The direction of force is 30 degree angle with the object movement direction. When the object reaches back to its initial location, how much work has been done on this object?  cos 30 J 2.0 J  cos 30 J 4.None of the above. CLICKER! Initial and final locations are the same. s = 0, so W = 0

A man is carrying a suitcase and walking along a straight line. If the suitcase weigh 20 N and the man walks a distance of 10 m, how much work has been done on the suitcase? J J 3.0 J 4.None of the above. CLICKER! W = F cos  s = F cos 90 s = 0 (cos 90 = 0)

Work F s θ = 180º W negative F s θ = 0º W positive F s θ = 90º W zero θ θ

A crate (weight=40N) is sliding down a ramp 10m long. The normal force on the crate is 30N. What is the work done by the normal force as it slides the length of the ramp? (1) -300J(2) -100J(3) 0J(4) 100J (5) 300J(6) 400J(7) 700J Force is perpendicular – cos(90) = 0 FNFN v CLICKER!

An box of 10 kg is kicked on a floor having a kinetic friction of 0.2. If the box moves 2 m before it comes to rest, what is the work done by the floor to the box? Example 1

An bullet of 0.2 kg has a speed of 100 m/s. What will be its kinetic energy? 1). 100 J 2). 200 J 3). 500 J 4). 1000J 5). 0 J CLICKER! K.E. = ½ mv 2 = ½ 0.2 x (100) 2 = 1000 J

Work-Kinetic Energy Work done by F NET,EXTERNAL (or ΣF) : (ΣF) s = (ma) s using const accel eqn's (see text) 2as = v f 2 - v 0 2 (ΣF)s = ½mv f 2 - ½mv 0 2 W NET = KE FINAL - KE INITIAL

Work done by gravity W g = mgh 0 - mgh f = PE 0 – PE f = ΔPE PE = mgh Must choose reference level –arbitrary choice –be consistent once select h Ref Level y=0 h y positive upwards

A crate of 1000 kg is lifted from the ground with a constant speed to a height of 10 m. What is the potential gain? Example 3

A 2000 kg car is driving with a speed of 30 m/s. The driver applies the break for a distance of 20 m to reduce the speed to 20 m/s. What is the force applied to the wheel-drum during this event? (Use work-energy theorem to solve). Example 4 F

A 100 kg crate is hanged from a bar as shown. (a) What is the potential energy of the crate with respect to the crane? (b) What is the potential energy of the crate with respect to the ground? Example 5 2 m 4 m

Which of the following path to lift a box from 1 st to the 2 nd floor will save the potential energy? 1.red 2.green 3.blue 4.The same at all paths. CLICKER!

Book A is raised from the floor to a point 2.0m above the floor. An identical book (B) is raised from a point 2.0m below the ceiling to the ceiling. Which book undergoes the greatest increase in gravitational potential energy? 1.Book A 2.Book B 3.Same for both books CLICKER!

A roller coaster is released along the track as shown. Which of the following statement for the kinetic energy is true? 1.A > B 2.C > B 3.E < C 4.D > A 5.The same at all locations. CLICKER! A B C D E

A roller coaster is released along the track as shown. Which of the following statement for the potential energy is true? 1.A > C 2.C > B 3.E < C 4.D > A 5.The same at all locations. CLICKER! A B C D E

A roller coaster is released along the track as shown. Which of the following statement for the total energy is true? 1.A > B 2.C > B 3.E < C 4.D > B 5.The same at all locations. CLICKER! A B C D E

A roller coaster starts from rest at point A. Find the speed of the roller coaster at the points B, C and D. Example 6 A B C D 10 m 8 m 6 m (The mass is not necessary to know).

3 balls of the same mass are thrown from a cliff, all with a speed of 25m/s. A is thrown upward at an angle of 45 . B is thrown horizontally. C is thrown downward at an angle of 45 . Which one is traveling fastest when it hits the ground? 1.A 2.B 3. C 4. All three are traveling the same speed Same initial KE, same change in PE, same increase in KE. Does the mass matter? Not in this case. It would cancel. E i = E f KE i + PE i = PE f + KE f + KE f ½ mv i 2 + mgh i = 0 + ½mv f 2 CLICKER!

Suppose I drop a 0.2kg mass ball from a height 3.0m above the floor. What is the speed of the ball just before it hits the floor? h=0m h=3m E i = E f KE i + PE f = KE f + PE f 0 + mgh = ½ mv Cancel m gh = ½v 2 2(9.8 m/s 2 )(3m) =v 2 v=7.7 m/s Example 7

A bead of 0.5 kg is released from rest onto a foam placed on the floor as shown. If the foam compresses 0.2m upon the impact of the bead, find the average force that the foam exerts the bead. The force is nonconservative. Example 8

At the same time that Stuntman A slides down the roof (starting from rest), Stuntman B steps off a roof (starting at the same height) on the other side of the street. Assume a 'no-friction' roof and negligible air resistance. Which Stuntman is traveling faster when they make contact with the pad? (1)A (2) B (3) both have the same speed Start at same height and initial speed, end at same height, same energy lost due to pad, no friction CLICKER!

At the same time that Stuntman A slides down the roof (starting from rest), Stuntman B steps off a roof (starting at the same height) on the other side of the street. If there is a ‘friction' between A and the roof, which Stuntman is traveling faster when they make contact with the pad? (1)A (2) B (3) both have the same speed CLICKER!

A bead of 0.5 kg is at ‘A’ is moved with an initial speed of ‘v A ’ along the track as shown. The track is frictionless except at the red strip near ‘C’, which has a kinetic friction of (1) What is the minimum speed of the bead at B so that it will not fall of the track? (2) Find the minimum initial speed for the bead so that it will not fall of from the track at B. (3) Find the speed of the bead at C. (4) If the bead flies of at the end of the track, how high it will reach at D? Example 9 A B C D

A car (2000 kg) starts from rest accelerates for a 200 m and reached 30 m/s speed. Then it continues to travel with the same speed for the rest of the journey. Find the power consumed by the engine during racing the speed. Example 10

Problem Cutnell A particle, starting from point A in the drawing, is projected down the curved runway. Upon leaving the runway at point B, the particle is traveling straight upward and reaches a height of 4.00m above the floor before falling back down. Ignore friction and air resistance. Find the speed of the particle at point A. v 0 = 4.4m/s Example 11