Two boxes are stacked on top of one another on the back of a flat bed truck on a level roadway.The coefficient of static friction between the boxes is ,and the coefficient of static friction between the bottom box and the bed of the truck is .What is the limiting acceleration the truck can undergo before one or both of the boxes start sliding if ?

Question

Two boxes are stacked on top of one another on the back of a flat bed truck on a level roadway.The coefficient of static friction between the boxes is  ,and the coefficient of static friction between the bottom box and the bed of the truck is  .What is the limiting acceleration the truck can undergo before one or both of the boxes start sliding if  ?

Quizplus · Accepted Answer

The limiting acceleration can be found by using the formula:
a = μg
where μ is the coefficient of static friction and g is the acceleration due to gravity (9.8 m/s^2).
For the top box to start sliding:
a < μtop g
For the bottom box to start sliding:
a < μbottom g
The limiting acceleration will be the minimum of the above two values.
Given:
μtop = 0.11
μbottom = 0.116
g = 9.8 m/s^2

Substituting the given values in the above formula:
For the top box to start sliding: 
a < 0.11 × 9.8 = 1.078 m/s^2
For the bottom box to start sliding:
a < 0.116 × 9.8 = 1.137 m/s^2
The limiting acceleration will be the minimum of the above two values:
a < 1.078 m/s^2
Thus, the limiting acceleration of the truck is 1.078 m/s^2. 
Therefore, the answer is C.

Two Boxes Are Stacked on Top of One Another on the Back