A crate rests on a flatbed truck which is initially traveling at 17.8 m/s on a level road. The driver applies the brakes and the truck is brought to a halt in a distance of 33.1 m. If the deceleration of the truck is constant, what is the minimum coefficient of friction between the crate and the truck that is required to keep the crate from sliding?

vf^2=vi^2+2ad

solve for a.
Then
forcefriction=masscrate*a you know a
mu*masscrate*g=masscrate*a
mu=a/g

To find the minimum coefficient of friction between the crate and the truck, we can use the concept of frictional force and Newton's second law of motion.

The frictional force between the crate and the truck is given by the equation:

frictional force = coefficient of friction × normal force

The normal force is the force exerted by the truck on the crate perpendicular to the contact surface. Since the crate is at rest, the normal force is equal to the weight of the crate:

normal force = mass of crate × acceleration due to gravity

Now, the acceleration of the crate is the same as the acceleration of the truck because they are in direct contact. The acceleration of the truck can be calculated using the formula:

final velocity² = initial velocity² + 2 × acceleration × distance

In this case, the final velocity is zero (since the truck comes to a halt), the initial velocity (Vi) is 17.8 m/s, and the distance (d) is 33.1 m. Rearranging the formula gives:

acceleration = (final velocity² - initial velocity²) / (2 × distance)

Substituting the given values:

acceleration = (0² - 17.8²) / (2 × 33.1)

Now we have the acceleration of the truck. We can use this value and the mass of the crate (which is not given in the problem) to find the normal force. Let's assume the mass of the crate (m) is 1 kg for calculation purposes.

normal force = mass of crate × acceleration due to gravity
= 1 kg × 9.8 m/s²

Finally, we can calculate the minimum coefficient of friction by rearranging the equation:

coefficient of friction = frictional force / normal force

Plugging in the values, we get:

coefficient of friction = frictional force / (1 kg × 9.8 m/s²)

Since the frictional force is equal to mass × acceleration, we can substitute that in the equation:

coefficient of friction = (mass of crate × acceleration) / (1 kg × 9.8 m/s²)

Now we have all the information to calculate the minimum coefficient of friction. Replace the mass of the crate with the actual value to obtain the final answer.

-2.96

-4.786