A flatbed truck carrying a crate is moving at a steady speed of 15 m/s . The driver applies the brakes to stop the truck. If the coefficient of static friction between the crate and the truck bed is 0.3 , what is the minimum stopping distance of the truck such that the crate does not slide forward? (Take g = 10 m/s ^2 )

Step-by-step solution

When the truck decelerates, a pseudo force acts on the crate in the forward direction. To prevent the crate from sliding, the pseudo force must not exceed the maximum static friction. Let the maximum deceleration of the truck be a . ma _s mg a _s g a_ max = 0.3 10 = 3 m/s ^2 Using the third equation of motion to find the minimum stopping distance S : v^2 = u^2 - 2aS 0 = (15)^2 - 2(3)S 6S = 225 S = 225 6 = 37.5 m The minimum stopping distance is 37.5 m . Answer: 37.5 m