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Work and Energy Problems

This problem explores the energy dynamics involved when a 50 kg diver steps off a 10 m diving board and eventually rests 5 m underwater. It calculates the average resistance force exerted by the water on the diver. Additionally, the scenario of a monkey on a sled moving up a 25° incline is analyzed, taking into account the initial speed, mass, and kinetic friction. These physics problems illustrate the principles of work, energy conservation, and forces in motion.

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Work and Energy Problems

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  1. Work and Energy Problems

  2. 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.

  3. #37,part 1 Work required to stop the diver W = Fdcosq W = (F)(5)(cos180) W = -5F 5 m

  4. #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

  5. 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?

  6. #39 vi = 4 m/s m = 20 kg m = 0.20 d h = d sin 25 o 25

  7. #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

  8. #39, part 3 W=ΔTE WFf =PEg – KE -35.5d =82.8d – 160 -118.3 d = -160 d = 1.4 m

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