Explanation Given information: The upgrade angle ( θ ) is 7 ° . The acceleration ( a level ) in a level section at a constant rate is 3 ft/s 2 . The speed ( v 0 ) at the level section of the bus is 60 mi/h. The speed ( v ) at the upgrade of the bus is 60 mi/h. Calculation: Write the equation of mass ( m ) of the bus. m = W g Here, W is the weight of the bus and g is the acceleration due to gravity. Consider the bus moves in level section. Sketch the free body diagram and kinetic diagram of the bus at the level section as shown in Figure (1). Here, P is the friction force on the wheel, N R is the normal force on the rear wheel, and N F is the normal force on the front wheel. Refer Figure (1), Apply Newton’s law of equation along horizontal axis. (Consider positive as right movement). Σ F x = m a P = m a Substitute W g for m and a level for a . P = W g a level Consider the bus moves in the upgrade section. Sketch the free body diagram and kinetic diagram of the bus at the upgrade section as shown in Figure (2). Here, P is the friction force on the wheel, N R ′ is the normal force on the rear wheel, N F ′ is the normal force on the front wheel, and a ′ is the deceleration of the bus on the upgrade. Refer Figure (2), Find the deceleration ( a ′ ) of the bus at upgrade. Apply Newton’s law of equation along horizontal axis. (Consider positive as right movement). Σ F x = m a P − W sin 7 ° = m a ′ Substitute W g a level for P and W g for m . W g a level − W sin 7 ° = W g a ′ 1 g a level − sin 7 ° = 1 g a ′ a ′ = a level − g sin 7 ° Substitute 3 ft/s 2 for a level and 32

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ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 12.1, Problem 12.5P

To determine

The distance traveled by the bus up the grade when its speed has decreased to 50 mi/h.

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Chapter 12.1, Problem 12.4P

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