Explanation Given information: The train is travelling down a percentage of grade ( G ) is 5 % . The initial velocity of the train carrying the baggage ( v 1 ) is 120 mi / hr . The final velocity of the train carrying the baggage ( v 2 ) is 60 mi / hr . The interval of time ( t ) is 12 sec . The acceleration due to gravity ( g ) is 32.2 ft / s 2 . Calculation: Show the impulse momentum diagram of the baggage with all the forces acting on it as Figure (1). Calculate the angle of the slope at which the train is travelling ( θ ) using the relation: tan θ = G Substitute 5 % for G . tan θ = 5 100 θ = tan − 1 ( 0.05 ) θ = 2.86 ° Convert the initial velocity of the train ( v 1 ) from mi / hr to ft / s : v 1 = ( v 1 ) mi / hr × ( 5280 ft 1 mi ) × ( 1 hr 3600 sec ) Here, ( v 1 ) mi / hr is the initial velocity of the train in mi / hr . Substitute 120 mi / hr for ( v 1 ) mi / hr . v 1 = 120 × ( 5280 ft 1 mi ) × ( 1 hr 3600 sec ) = 176 ft / s Convert the final velocity of the train ( v 2 ) from mi / hr to ft / s : v 2 = ( v 2 ) mi / hr × ( 5280 ft 1 mi ) × ( 1 hr 3600 sec ) Here, ( v 2 ) mi / hr is the final velocity of the train in mi / hr . Substitute 60 mi / hr for ( v 2 ) mi / hr . v 2 = 60 × ( 5280 ft 1 mi ) × ( 1 hr 3600 sec ) = 88 ft / s The expression for initial momentum ( P 1 ) of the baggage as follows: P 1 = m v 1 The expression for final momentum of the baggage ( P 2 ) as follows: P 2 = m v 2 Calculate the normal force ( N ) by resolving the forces in the Y -direction using the relation: Σ F y = 0 N − m g cos θ = 0 N = m g cos θ Calculate the horizontal force ( F x ) by resolving the forces in X-direction using the relation: Σ F x = m g sin θ − μ s N Substitute m g cos θ for N

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ISBN: 9781260804638

Author: BEER

Publisher: MCG

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Chapter 13.3, Problem 13.125P

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Find the smallest allowable value of the coefficient of static friction between a trunk and the floor of the baggage car (μs).

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Chapter 13.3, Problem 13.124P

Chapter 13.3, Problem 13.126P

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Find the smallest allowable value of the coefficient of static friction between a trunk and the floor of the baggage car ( μ s ) .

Solution Summary: The author calculates the angle of the slope at which the train is travelling using the relation: lmathrmtantheta =G Substi

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Find the smallest allowable value of the coefficient of static friction between a trunk and the floor of the baggage car (μs).

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