Work and Energy Problems

A 50 kg diver steps off a 10 m high diving board and drops straight down into the water. If the diver comes to rest 5 m below the surface of the water, determine the average resistance force exerted on the diver by the water.

#37,part 1 Work required to stop the diver W = Fdcosq W = (F)(5)(cos180) W = -5F 5 m

Set PE=0 at bottom, KE= 0 at bottom #37, part 2 W = DTE Set PE=0 at bottom, KE= 0 at bottom ΔTE = 0 - PE at top of tower PEg = (50)(9.8)(15) = 7350 J ΔTE = -7350 W = -7350 -5F = -7350 F = 1470 N

In a circus performance, a monkey on a sled is given an initial speed of 4 m/s up a 25º incline. The combined mass of the monkey and the sled is 20 kg, and the coefficient of kinetic friction between the sled and the incline is 0.20. How far up the incline does the sled move?

#39 vi = 4 m/s m = 20 kg m = 0.20 d h = d sin 25 o 25

WFf =(0.2)(20)(9.8)(cos25)(d)(-1)= -35.5d #39, part 2 W = ΔTE = PEg - KE PEg = (20)(9.8)(dsin25) = 82.8 d KE = ½ (20)(4)2 = 160J WFf = Ff(d)(cos180) Ff = µmgcosθ WFf =(0.2)(20)(9.8)(cos25)(d)(-1)= -35.5d

#39, part 3 W=ΔTE WFf =PEg – KE -35.5d =82.8d – 160 -118.3 d = -160 d = 1.4 m