PHYS 1401 College Physics I CRN 55178 HOMEWORK PROBLEMS Khalid Bukhari HW 5 Chapter 5 ENERGY PART A Hand in your answers in class on scantron on Monday 04 October 2010 1 A worker pushes a wheelbarrow 5 0 m along a level surface exerting a constant horizontal force of 50 0 N If a frictional force of 43 N acts on the wheelbarrow in a direction opposite to that of the worker what net work is done on the wheelbarrow a 250 J b 215 J c 35 J d 15 J e 45 J Wnet Wapplied W friction F cos 0 D x f cos 180 D x force F f Dx 50 0 N 43 N 5 0 m 35 J 2 A skier leaves a ski jump at 15 0 m s at some angle At what speed is he traveling at his maximum height of 4 50 m above the level of the end of the ski jump Neglect air friction a 11 7 m s b 16 3 m s c 12 2 m s d 8 55 m s e 17 4 m s In the absence of any air resistance the work done by nonconservative forces is zero The work energy theorem then states that KE ffi PE KE PEi which becomes 1 1 m v2f m gy f m vi2 m gyi 2 2 or v fi v 2 2 g yi y f Choosing the initial point to be where the skier leaves end of the jump and the final point where he reaches maximum height this yields vf 15 0 2 m s 2 9 80 m s2 4 50 m 11 7 m s making a the correct answer 3 A 40 0 N crate starting at rest slides down a rough 6 00 m long ramp inclined at 30 0 with the horizontal The magnitude of the force of friction between the crate and the ramp is 6 0 N What is the speed of the crate at the bottom of the incline a 1 60 m s b 3 32 m s c 4 5 m s d 6 42 m s e 7 75 m s The mass of the crate is m w g 40 0 N 9 80 m s2 4 08 kg and we may write the work energy theorem as Wnet Wfric Wgrav KE fi KE 1 2 Since the crate starts from rest KEi 2 m vi 0 and we are left with KE f Wfric Wgrav fk cos180 Dx w cos 60 0 Dx so KE f 6 00 N 6 00 m 40 0 N cos 60 0 6 00 m 36 0 J 120 J 84 0 J 1 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 5 and vf 2 KE f m 2 84 0 J 4 08 kg 6 42 m s making choice d the correct response 4 What average mechanical power must be delivered by the muscles of a 70 0 kg mountain climber who climbs a summit of height 325 m in 95 0 min Note Due to inefficiencies in converting chemical energy to mechanical energy the amount calculated here is only a fraction of the power that must be produced by the climber s body See Chapter 12 a 39 1 W b 54 6 W c 25 5 W d 67 0 W e 88 4 W We assume the climber has negligible speed at both the beginning and the end of the climb Then KE fi KE 0 and the work done by the muscles is Wnc 0 PE fi PE mg y fi y 70 0 kg 9 80 m s 325 m 2 23 10 2 5 J The average power delivered is P Wnc 2 23 105 J 39 1 W Dt 95 0 min 60 s 1 min and the correct answer is choice a 5 The work required to accelerate an object on a frictionless surface from a speed v to a speed 2v is a equal to the work required to accelerate the object from v 0 to v b twice the work required to accelerate the object from v 0 to v c three times the work required to accelerate the object from v 0 to v d four times the work required to accelerate the object from 2v to 3v or e not known without knowledge of the acceleration The net work needed to accelerate the object from 0 to is W1 KE fi KE 21 m v2 1 2 m 0 2 21 m v2 The work required to accelerate the object from speed to speed 2 is 2 W2 KE fi KE 12 m 2 v 1 2 m v2 12 m 4 v 2 v2 3 1 2 m v 2 3W1 Thus the correct choice is c 6 Alex and John are loading identical cabinets onto a truck Alex lifts his cabinet straight up from the ground to the bed of the truck whereas John slides his cabinet up a rough ramp to the truck Which statement is correct a Alex and John do the same amount of work b Alex does more work than John c John does more work than Alex d None of these statements is necessarily true because the force of friction is unknown e None of these statements is necessarily true because the angle of the incline is unknown 2 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 5 Assuming that the cabinet has negligible speed during the operation all of the work Alex does is used increasing the gravitational potential energy of the cabinet However in addition to increasing the gravitational potential energy of the cabinet by the same amount as Alex did John must do work overcoming the friction between the cabinet and ramp This means that the total work done by John is greater than that done by Alex and the correct answer is c 7 Mark and David are loading identical cement blocks onto David s pickup truck Mark lifts his block straight up from the ground to the truck whereas David slides his block up a ramp on massless frictionless rollers Which statement is true a Mark does more work than David b Mark and David do the same amount of work c David does more work than Mark d None of these statements is necessarily true because the angle of the incline is unknown e None of these statements is necessarily true because the mass of one block is not given Since the rollers on the ramp used by David were frictionless he did not do any work overcoming nonconservative forces as he slid the block up the ramp Neglecting any change in kinetic energy of the block either because the speed was constant or was essentially zero during the lifting process the work done by either Mark and David equals the increase in the gravitational potential energy of the block as it is lifted from the ground to the truck bed Because they lift identical blocks through the same vertical …