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Mechanics resolving forces problem

There's a particle P on an inclined plane of 30 degrees to the horizontal. A force of 36N is applied to the particle at an angle of 30 to the parallel slope. The particle is moving at a constant velocity so is at an equilibrium.

Find the normal reaction force between P and the plane.
To find the reaction, I tried 2 ways: resolving perpendicular to the slope and resolving vertically but both yield difference answers.

Resolving perpendicular:
R+36sin30=4gcos30
R=16N which is the correct answer

Resolving vertically:
Rsin60+36sin60=4g
R=9.31N

What have I done wrong?
Have you drawn a diagram? That always helps with mechanics
Original post by 29Bilal96
Have you drawn a diagram? That always helps with mechanics


I did, that's how I worked out which angles to use when resolving :cool:
Original post by BP_Tranquility
There's a particle P on an inclined plane of 30 degrees to the horizontal. A force of 36N is applied to the particle at an angle of 30 to the parallel slope. The particle is moving at a constant velocity so is at an equilibrium.

Find the normal reaction force between P and the plane.
To find the reaction, I tried 2 ways: resolving perpendicular to the slope and resolving vertically but both yield difference answers.

Resolving perpendicular:
R+36sin30=4gcos30
R=16N which is the correct answer

Resolving vertically:
Rsin60+36sin60=4g
R=9.31N

What have I done wrong?


I suspect there is a friction force which would come into your vertical resolution but not the perpendicular one

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