homework8-solutions

homework8-solutions - ME 104 Homework 8 Solutions Prof Karl...

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ME 104: Homework 8 Solutions Prof. Karl Hedrick: University of California, Berkeley

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Chapter 16, Solution 3 For the board to remain in the position shown, we need 0. B \$ When the board is just about to start rotating about A , we have 0. B eff ( ) : A A M M   (3 ft)cos78 (3 ft)sin 78 W W a g   2 cot 78 (32.2 ft/s )cot 78 a g   2 6.84 ft/s a
Chapter 16, Solution 5 ( a ) Four-wheel drive: 0: 0 y A B A B F N N W N N W mg Thus: ( ) 0.80 A B k A k B k A B k F F N N N N W mg eff ( ) : x x A B F F F F ma   0.80 mg ma 2 0.80 0.80(32.2 ft/s ) a g 2 25.8 ft/s a ( b ) Rear-wheel drive: eff ( ) : (40 in.) (100 in.) (20 in.) B B A M M W N ma     0.4 0.2 A N W ma Thus: 0.80(0.4 0.2 ) 0.32 0.16 A k B F N W ma mg ma eff ( ) : x x A F F F ma   0.32 0.16 0.32 0.84 mg ma ma g a 2 0.32 (32.2 ft/s ) 0.84 a 2 12.27 ft/s a

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( c ) Front-wheel drive: eff ( ) : (100 in.) (60 in.) (20 in.) A A B M M N W ma     0.6 0.2 B N W ma Thus: 0.80(0.6 0.2 ) 0.48 0.16 B k B F N W ma mg ma eff ( ) : x x B F F F ma   2 0.48 0.16 0.48 1.16 0.48 (32.2 ft/s ) 1.16 mg ma ma g a a 2 13.32 ft/s a
Chapter 16, Solution 13 Kinematics: Assume that the barrel is sliding, but not tipping. 0 G a a a Since the cord is inextensible, C a a Kinetics: Draw the free body diagrams of the barrel and the cylinder. The barrel is sliding. 0.35 F k F N N Assume that tipping is impending, so that the line of action of the reaction on the bottom of the barrel passes through Point B . 10 in. e For the barrel. 0: 0 y B B F N W N W 0: 4 (18)(0.35 ) 0 G M Ne T N (18)(0.35) 10 6.3 0.925 4 4 B B e T N W W : 0.35 B B x W W F a T N a g g 0.35 0.925 0.35 0.575 B B a T N g W W For the cylinder: : C C C W a F a W T W g g 0.925 (2.1765)(200 lb) 1 0.575 1 B C W T W a g 435 lb C W

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Chapter 16, Solution 34 Case 1: Case 2: Case 3: ( a ) 2 0 0 eff 9 ( ) : (160 lb) ft (15 lb ft s ) 12 M M   2 8 rad/s α ( b ) 9 12 10 ft 13.333 rad ft
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