GATE ME 2014 Set 2 — Question 46
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Engineering Mechanics → Dynamics → Dynamics of Rigid Bodies
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Question
A truck accelerates up a incline with a crate of 100 kg. Value of static coefficient of friction between the crate and the truck surface is 0.3. The maximum value of acceleration (in ) of the truck such that the crate does not slide down is _______
Correct answer
1 to 1.3
Solution
Let be the acceleration of the truck up the incline.
For the crate (mass ) not to slide down, we consider the forces acting on it in the frame of the truck:
To prevent sliding, the friction force must be less than or equal to the limiting static friction:
Substituting the values (, ):
The maximum acceleration is approximately , which falls within the range of 1.0 to 1.3.
For the crate (mass ) not to slide down, we consider the forces acting on it in the frame of the truck:
1.Pseudo force: acting down the incline.
2.Gravity component: acting down the incline.
3.Normal force: acting perpendicular to the incline.
4.Friction force: acting up the incline to oppose the tendency to slide down.
For the crate to remain stationary relative to the truck:To prevent sliding, the friction force must be less than or equal to the limiting static friction:
Substituting the values (, ):
The maximum acceleration is approximately , which falls within the range of 1.0 to 1.3.
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