I was surfing through an Olympiad paper and I was caught with this question.

A block of mass 1 kg is stationary with respect to a conveyor belt that is accelerating with $1\, \tfrac{m}{s^2}$ upwards at an angle of 30° as shown in figure. Determine force of friction on block and contact force between the block & belt. (I don't have enough reputation to post a diagram)

I tried to split the normal forces and proceed using the pseudo force method but am stuck on how to do so.

Any other methods so as to proceed in this problem?

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    $\begingroup$ Hi user24613. Welcome to Phys.SE. If you haven't already done so, please take a minute to read the definition of when to use the homework tag, and the Phys.SE policy for homework-like problems. $\endgroup$ – Qmechanic May 17 '13 at 17:43
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    $\begingroup$ I've edited the question to give a more descriptive title. $\endgroup$ – Ben Crowell May 17 '13 at 17:43
  • $\begingroup$ @qmechanic: sorry for the misunderstanding. i was actually aware of the concept but the intricacies in it is what made me post the question. i have been stuck with this question for a pretty long time . i am now aware of the rules. hereafter will abide by them $\endgroup$ – user24613 May 17 '13 at 17:51
  • $\begingroup$ @greg: i have accidentally deleted your answer. can you post it once more? $\endgroup$ – user24613 May 17 '13 at 18:01
  • $\begingroup$ @user24613: I've never heard of the term 'pseudo force method,' can you explain what that means? Does it by any chance refer to separating a force into its components? Because imo the component forces are just as real as the resultant force. $\endgroup$ – Greg May 17 '13 at 20:54

The block is accelerating at $1\frac{m}{s^2}$ up the incline, since it is stationary with respect to the conveyor belt. What force is causing the block to accelerate? It can't be the normal force (which acts perpendicular to the motion). It must be the frictional force, which counteracts the component of gravity parallel to the incline.

Using Newton's second law of motion, sum up the forces that are parallel to the incline. You should be able to solve for $F_{friction}$. $$\sum F_\parallel = ma_\parallel$$

Do the same for the forces perpendicular to the incline. Is the block accelerating in the direction perpendicular to the incline? What does that say about the forces that are acting in this direction? Using Newton's second law once again, you can solve for $F_{normal}$. $$\sum F_\perp=0$$


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