Determine the magnitude of the total force exerted by the track on the

[TheDudeTR]

Homework Statement

i did not understand free body diagram in this question

Relevant Equations

F = ma

This is the question.

This is the FBD in the solution given. What i didn't understand is the sense of normal force. in the question mg force pulls particle down and according to my logic normal vector should be upwards in this conditions. but it is downwards in the given FBD. when i try to solve question with my own way result is different because of in the question it takes normal axis equations as (N+mg.cos30=m*a) and i took it as (-N+mg.cos30=m*a ) where am i wrong? can you help me please.

 

[haruspex]

the sense of normal force

In principle it could be either way - depends on the speed and the radius, etc.
But you do not need to care which way it is when drawing the diagram. If you chose wrongly it will come out negative, but the frictional force only cares about the magnitude.