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CHAPTER 4

# CHAPTER 4 - PROBLEM 4.1 The boom on a 4300-kg truck is used...

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PROBLEM 4.1 The boom on a 4300-kg truck is used to unload a pallet of shingles of mass 1600 kg. Determine the reaction at each of the two ( a ) rear wheels B , ( b ) front wheels C. SOLUTION () ( ) 2 1600 kg 9.81 m/s AA Wm g == 15696 N = or 15.696 kN A = W ( ) 2 4300 kg 9.81 m/s GG g 42 183 N = or 42.183 kN G = W ( a ) From f.b.d. of truck with boom ( ) ( ) ( ) 0: 15.696 kN 0.5 0.4 6cos15 m 2 0.5 0.4 4.3 m CB MF  Σ= ++ °  ( )( ) 42.183 kN 0.5 m 0 += 126.185 2 24.266 kN 5.2 B F ∴= = or 12.13 kN B = F W ( b ) From f.b.d. of truck with boom ( ) ( ) ( ) ( ) 0: 15.696 kN 6cos15 4.3 m 42.183 kN 4.3 0.4 m B M ° + ( ) 24 . 3 0 . 9 m 0 C F = 174.786 2 33.613 kN 5.2 C F = or 16.81 kN C = F W Check: ( ) 0: 33.613 42.183 24.266 15.696 kN 0? y F + = ( ) 57.879 57.879 kN 0 ok −=

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PROBLEM 4.2 Two children are standing on a diving board of mass 65 kg. Knowing that the masses of the children at C and D are 28 kg and 40 kg, respectively, determine ( a ) the reaction at A , ( b ) the reaction at B . SOLUTION () ( ) 2 65 kg 9.81 m/s 637.65 N GG Wm g == = ( ) 2 28 kg 9.81 m/s 274.68 N CC g = ( ) 2 40 kg 9.81 m/s 392.4 N DD g = ( a ) From f.b.d. of diving board ( ) ( )( ) ( )( ) ( )( ) 0: 1.2 m 637.65 N 0.48 m 274.68 N 1.08 m 392.4 N 2.08 m 0 By MA Σ= = 1418.92 1182.43 N 1.2 y A ∴= = or 1.182 kN y = A W ( b ) From f.b.d. of diving board ( ) ( ) ( ) ( ) 0: 1.2 m 637.65 N 1.68 m 274.68 N 2.28 m 392.4 N 3.28 m 0 Ay MB = 2984.6 2487.2 N 1.2 y B = or 2.49 kN y = B W Check: ( ) 0: 1182.43 2487.2 637.65 274.68 392.4 N 0? y F + = ( ) 2487.2 2487.2 N 0 ok −=
PROBLEM 4.3 Two crates, each weighing 250 lb, are placed as shown in the bed of a 3000-lb pickup truck. Determine the reactions at each of the two ( a ) rear wheels A , ( b ) front wheels B . SOLUTION ( a ) From f.b.d. of truck ( )( ) ( )( ) ( )( ) ( )( ) 0: 250 lb 12.1ft 250 lb 6.5 ft 3000 lb 3.9 ft 2 9.8 ft 0 B A MF Σ= + + = 16350 2 1668.37 lb 9.8 A F ∴= = 834 lb A F W ( b ) From f.b.d. of truck ( )( ) ( )( ) ( )( ) ( )( ) 0: 2 9.8 ft 3000 lb 5.9 ft 250 lb 3.3 ft 250 lb 2.3 ft 0 AB + = 17950 2 1831.63 lb 9.8 B F = 916 lb B F W Check: ( ) 0: 250 1668.37 250 3000 1831.63 lb 0? y F − + − − + = ( ) 3500 3500 lb 0 ok −=

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PROBLEM 4.4 Solve Problem 4.3 assuming that crate D is removed and that the position of crate C is unchanged. P4.3 The boom on a 4300-kg truck is used to unload a pallet of shingles of mass 1600 kg. Determine the reaction at each of the two ( a ) rear wheels B , ( b ) front wheels C SOLUTION ( a ) From f.b.d. of truck ( )( ) ( )( ) ( )( ) 0: 3000 lb 3.9 ft 2 9.8 ft 250 lb 12.1ft 0 BA MF Σ= + = 14725 2 1502.55 lb 9.8 A F ∴= = or 751lb A = F W ( b ) From f.b.d. of truck ( )( ) ( )( ) ( )( ) 0: 2 9.8 ft 3000 lb 5.9 ft 250 lb 2.3 ft 0 AB + = 17125 2 1747.45 lb 9.8 B F = or 874 lb B = F W Check: ( ) 0: 2 751 874 3000 250 lb 0? y F  + =  ( ) 3250 3250 lb 0 ok −=
PROBLEM 4.5 A T-shaped bracket supports the four loads shown. Determine the reactions at A and B if ( a ) 100 mm, a = ( b ) 70 mm. a = SOLUTION ( a ) From f.b.d. of bracket ( )( ) ( )( ) ( )( ) ( ) 0: 10 N 0.18 m 30 N 0.1 m 40 N 0.06 m 0.12 m 0 B MA Σ= + + = 2.400 20 N 0.12 A ∴= = or 20.0 N = A W ( ) ( )( ) ( )( ) ( )( ) ( )( ) 0: 0.12 m 40 N 0.06 m 50 N 0.12 m 30 N 0.22 m 10 N 0.3 m 0 A MB Σ = −−−− = 18.000 150 N 0.12 B = or 150.0 N = B W ( b ) From f.b.d. of bracket ( )( ) ( )( ) ( )( ) ( ) 0: 10 N 0.15 m 30 N 0.07 m 40 N 0.06 m 0.12 m 0 B + + = 1.200 10 N 0.12 A = or 10.00 N = A W ( ) ( )( ) ( )( ) ( )( ) 0: 0.12 m 40 N 0.06 m 50 N 0.12 m 30 N 0.19 m A ( )( ) 10 N 0.27 m 0 −= 16.800 140 N 0.12 B = or 140.0 N = B W

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PROBLEM 4.6 For the bracket and loading of Problem 4.5, determine the smallest distance a if the bracket is not to move. P4.5 A T-shaped bracket supports the four loads shown. Determine the reactions at A and B if ( a ) 100 mm, a = ( b ) 70 mm. a = SOLUTION The min a value will be based on 0 = A From f.b.d. of bracket ( )( ) ( )( ) ( )( ) 0: 40 N 60 mm 30 N 10 N 80 mm 0 B Ma a Σ= + = 1600 40 mm 40 a ∴= = or min 40.0 mm a = W
PROBLEM 4.7 A hand truck is used to move two barrels, each weighing 80 lb.

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CHAPTER 4 - PROBLEM 4.1 The boom on a 4300-kg truck is used...

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