A flatbed truck is carrying a 20-kg crate up a sloping road. The coefficient of static friction between the crate and the bed is 0.40, and the coefficient of kinetic friction is 0.30. What is the maximum angle of slope that the truck can climb at constant speed if the crate is to stay in place

The angle is  

Explanation:

From the question we are told that

   The mass of the crate is  

   The coefficient of static friction is  

   The  coefficient of kinetic friction is  

Generally  for the the crate not to slip , the static frictional  must be equal to the force driving the truck

   i.e

Now since we are considering a slope that static frictional force is mathematically represented as

While the force driving the truck is mathematically represented as

Here  mg is the weight of the crate  so

         So

=>            

=>          

=>          

=>          

A diagram show an illustration is on the first uploaded image

the area between the graph and the t axis

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