A 22 kg box rests on the back of a truck. The

coefficient of static friction between the box
and the truck bed is 0.369.
The acceleration of gravity is 9.81 m/s2 .
What maximum acceleration can the truck
have before the box slides backward

To calculate the maximum acceleration that the truck can have before the box slides backward, we can use the equation for static friction:

\(f_{\text{{friction}}} = \mu_{\text{{static}}} \cdot f_{\text{{normal}}}\)

where:
\(f_{\text{{friction}}}\) is the frictional force,
\(\mu_{\text{{static}}}\) is the coefficient of static friction, and
\(f_{\text{{normal}}}\) is the normal force.

The normal force is equal to the weight of the box, which can be calculated as:

\(f_{\text{{normal}}} = m \cdot g\)

where:
\(m\) is the mass of the box, and
\(g\) is the acceleration due to gravity.

Substituting the values into the equations, we get:

\(f_{\text{{normal}}} = 22 \, \text{{kg}} \cdot 9.81 \, \text{{m/s}^2}\)

\(f_{\text{{friction}}} = 0.369 \cdot f_{\text{{normal}}}\)

Now, to find the maximum acceleration, we replace \(f_{\text{{normal}}}\) in the first equation with \(f_{\text{{friction}}}\):

\(f_{\text{{friction}}} = m \cdot g \cdot a_{\text{{max}}}\)

where:
\(a_{\text{{max}}}\) is the maximum acceleration.

Substituting the values, we get:

\(0.369 \cdot 22 \, \text{{kg}} \cdot 9.81 \, \text{{m/s}^2} = 22 \, \text{{kg}} \cdot 9.81 \, \text{{m/s}^2} \cdot a_{\text{{max}}}\)

Simplifying the equation, we find:

\(0.369 = a_{\text{{max}}}\)

Therefore, the maximum acceleration the truck can have before the box slides backward is \(0.369 \, \text{{m/s}^2}\).

To find the maximum acceleration of the truck before the box slides backward, we need to compare the force of static friction between the box and the truck bed with the maximum frictional force.

The maximum frictional force can be calculated using the equation:

F_friction_max = coefficient_of_static_friction * Normal_force

The normal force is equal to the weight of the box, which is given by:

Normal_force = mass * acceleration_due_to_gravity

Plugging in the values given:

mass = 22 kg
coefficient_of_static_friction = 0.369
acceleration_due_to_gravity = 9.81 m/s^2

Normal_force = 22 kg * 9.81 m/s^2 ≈ 215.82 N

Now, we can calculate the maximum frictional force:

F_friction_max = 0.369 * 215.82 N ≈ 79.69 N

The maximum acceleration can then be found using Newton's second law of motion:

F_friction_max = mass * acceleration

Rearranging the equation to solve for acceleration:

acceleration = F_friction_max / mass

Substituting the values:

acceleration = 79.69 N / 22 kg ≈ 3.62 m/s^2

Therefore, the maximum acceleration the truck can have before the box slides backward is approximately 3.62 m/s^2.

Wb = mg = 22kg * 9.8N/kg = 215.6N. =

Weight of box.

Fb = (215.6N,0 deg).

Fp = Fh = 215.6sin(0)= 0 = Force paral-
lel to plane = Hor. force.

Fv = 215.6cos(0) = 215.6N. = Force perpendicular to plane = Normal.

Ff = u*Fv = 0.369 * 215.6 = 79.56N. =
Force due to friction.

Fn = Fp - Ff = 22a,
0 - 79.56 = 22a,
a = -3.62m/s^2.

Post it.