Question

The log has a mass of m = 954 kg; the truck has a mass of M = 8950 kg. According to the truck manufacturer, the truck can accelerate from 0 to 55 mph in 27.0 seconds, but this does not account for the additional mass of the log. Calculate the minimum coefficient of static friction μs needed to keep the log in the back of the truck.

Answer 1

There's a lot going on in this problem so it would be helpful to break it up into manageable chunks.

Lets start by finding the force that the truck can output. We are given the mass and we can find the acceleration of the truck, so we can use Newton's Second Law (F = m*a) to find the force output of the truck.

We also know that acceleration, assuming it is constant, can be found by finding the rate of change of the velocity. We know that the truck starts at rest (v=0) and can accelerate to v = 55 mph (which you would have to convert to m/s to keep standard units!) in 27 seconds. For constant acceleration: a = (v2-v1)/t

With all that done, you have the force that the truck can travel with. Now take that force, and use the mass of the truck+ the log to find the loaded acceleration

Once you have your loaded acceleration, go back to newtons 2nd law to compute the force required to keep the log accelerating at that rate.

Finally, you have to know that friction force is equal to the normal force times the coefficient of friction.

Ff = N*u_f

We also know that Normal force = mass * gravity
so:
Ff = m_log * g * u_f

You should have everything at this point and you can solve for the coefficient of friction!

Good luck, let me know if you have any questions

Answer 2

Thank you so much, that was perfect!