Why Does the Ramp Exert Total Force mg Instead of mgcos30 on the Mass?

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The total force exerted by the ramp on the mass is equal to mg, not mg cos30, as clarified in the discussion. The normal force, which is mg cos30, only accounts for the perpendicular component of the gravitational force acting on the block. Since the block is stationary, the total force must balance the gravitational force, leading to the conclusion that the ramp exerts a total force of mg to maintain equilibrium. This distinction is crucial for understanding the dynamics of forces on inclined planes.

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My exam is in an hour, so quick replies are dearly needed!

http://www.ph.qmul.ac.uk/phy116/Exams/Mid%20Term%20Test%202006%20Answers.pdf
Question 3)a

I would have said the force exerted by the RAMP on the MASS is mgcos30, not mg as my lecturer has said (and it's the same in every paper).

What am I not seeing here? The only thing I can think of is due to the axis of where F is.

Thanks!
 
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The block is not moving, thus a = 0. Also, gravity pulls down on the block with a force equal to mg. If you accept these two facts, balance the forces in the vertical direction and see what you get.
 
I just saw this post, too late for the exam, but I have a comment that may help.

mg cos30 is the normal force exerted by the ramp on the block. But the question is really asking for the total force F exerted by the ramp, which includes the friction and normal forces.

As diazona said, F must balance against the downward, vertical force mg.
 

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