(a) Explanation Given information: The angle ( θ ) is 6 ° . The initial velocity of the bus ( v 1 ) is 80 km / hr . The final velocity of the bus ( v 2 ) is 100 km / hr . The time ( t ) still on the level section of the highway is 8 sec . Initially the time ( t ) is 0. The acceleration due to gravity ( g ) is 9.81 m / s 2 . Calculation: Show the impulse momentum diagram for accelerating on level ground as Figure (1). Convert the initial velocity of the bus ( v 1 ) from km / hr to m / s : v 1 = ( v 1 ) km / hr × ( 1000 m 1 km ) × ( 1 hr 3600 sec ) Here, ( v 1 ) km / hr is the initial velocity of the bus in km / hr . Substitute 80 km / hr for ( v 1 ) km / hr . v 1 = 80 × ( 1000 m 1 km ) × ( 1 hr 3600 sec ) = 22.222 m / s Convert the final velocity of the bus ( v 2 ) from km / hr to m / s : v 2 = ( v 2 ) km / hr × ( 1000 m 1 km ) × ( 1 hr 3600 sec ) Here, ( v 2 ) km / hr is the final velocity of the bus in km / hr . Substitute 100 km / hr for ( v 2 ) km / hr . v 2 = 100 × ( 1000 m 1 km ) × ( 1 hr 3600 sec ) = 27.778 m / s Consider the Impulse momentum in the x direction while on level ground. Calculate for initial momentum ( P 1 ) of the bus using the relation: P 1 = m v 1 Substitute 22.222 m / s for v 1 . P 1 = m ( 22.222 m / s ) = 22.222 m Calculate the final momentum of the bus ( P 2 ) using the relation: P 2 = m v 2 Substitute 27.778 m / s for v 2 . P 2 = m ( 27.778 m / s ) = 27.778 m The expression for the impulse acting upon the load while the bus comes to rest ( ∑ Imp ( 1 − 2 ) ) as follows: ∑ Imp ( 1 − 2 ) = ∫ 0 t F d t The expression for the impulse momentum as follows: P 1 + ∑ Imp ( 1 − 2 ) = P 2 Substitute 22 (b) To determine Find the time ( t ) when the speed is 60 km / h .

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 13.3, Problem 13.128P

(a)

To determine

Find the speed of the bus (v3) when t=10sec.

(b)

To determine

Find the time (t) when the speed is 60km/h.

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Chapter 13.3, Problem 13.127P

Chapter 13.3, Problem 13.129P

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Find the speed of the bus ( v 3 ) when t = 10 sec .

Solution Summary: The author shows the impulse momentum diagram for accelerating on level ground as Figure (1).