Question

You have been hired to help improve the material movement system at a manufacturing plant. Boxes containing 22 𝑘𝑔 of tomato sauce in glass jars must slide from rest down a frictionless roller ramp to the loading dock, but they must not accelerate at a rate that exceeds 2.5 𝑚/𝑠 2 because of safety concerns. (a) What is the maximum angle of inclination of the ramp? (b) If the vertical distance the ramp must span is 1.2 𝑚, with what speed will the boxes exit the bottom of the ramp? (c) What is the normal force on a box as it moves down the ramp?

Answer 1

So, we can obtain the equation of motion using 2 nd Newton law:

$Ma = Mgsin(a)$

We can obtain the estimation of a from this statement:

$a\in(0,arcsin(0.25))$

The reaction force acting on the body :

$N = 55\sqrt {15}$