Consider a large truck carrying a heavy load, such as steel beams. A significant

Question

Consider a large truck carrying a heavy load, such as steel beams. A significant hazard for the driver is that the load may slide forward, crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, that a 14,000-kg load sits on the flatbed of a 20,000-kg truck moving at 12.0 m/s. Assume the load is not tied down to the truck and has a coefficient of static friction of 0.400 with the truck bed.

(a) Calculate the minimum stopping distance for which the load will not slide forward relative to the truck.
m

(b) Is any piece of data unnecessary for the solution? (Select all that apply.)
mass of the load
mass of the truck
velocity
coefficient of static friction
all are necessary

Explanation / Answer

The only thing holding the load in place is friction. That formula is Ff = Fn.

Since we do not want the load to move, we need the force of friction to equal the Force exerted when the truck slows down. That will be found as Fexerted = ma

Since those two forces must be equal, we can say

Fexerted = Ff

Substitutin leaves

ma = Fn

Now we also know that Fn means Force normal, that the force normal, on the flat surface of the truck bed, is equal to the weight (mg) of the load

Now we can say

ma = mg

Notice the m cancels out, so we didn't even need the mass of the load

a = g = (.4)(9.8) = 3.92 m/s2

That a is actually negative since the truck is slowing. Its a deceleration.

Now we can use that acceleration to determine the stopping distance for the truck

Since the truck is moving at 12 m/s we have initial velocity. When it stops the final velocity will be zero, and we calculated the acceleration (which is actually a deceleration)

Using Vf2 = Vo2 + 2ad will allow us to find the distance

0 = 122 + 2(-3.92)(d)

d = 18.37 m

Finally, notice that we only used the coefficient of friction, the initial velocity of the truck, and gravity to solve the problem

We did not need the mass of the truck or the mass of the load.

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