A flatbed truck is carrying a 20.0-kg crate up a sloping road inclined 15.0° above the horizontal. The coefficient of static friction between the crate and the bed is 0.400. What is the maximum acceleration that the truck can have if the crate is to stay in place? A) 0.625 m/s² B) 1.25 m/s² C) 2.50 m/s² D) 3.16 m/s² E) 6.33 m/s²

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Quizplus · Accepted Answer

The maximum static friction force can be calculated using the formula $ f_s = \mu_s \cdot N $, where $ N $ is the normal force. The normal force is $ N = mg \cos(\theta) $. The force down the slope is $ mg \sin(\theta) $. The maximum acceleration $ a $ is when the net force $ f_s = ma $. Solving for $ a $ gives $ a = g(\mu_s \cos(\theta) - \sin(\theta)) $. Substituting the given values results in $ a = 1.25 \, \text{m/s}^2 $.

A Flatbed Truck Is Carrying a 20