a 100 N block on a 30 degree incline, is being held motionless by friction. The coefficient of static friction between the block and the plane is 0.60. The force due to friction is?

I'm not sure how to get the answer which is 50 N. If someone could show me the work need to be done to get this answer. Thanks

Question

04-04-2018
Physics

contestada

a 100 N block on a 30 degree incline, is being held motionless by friction. The coefficient of static friction between the block and the plane is 0.60. The force due to friction is?

I'm not sure how to get the answer which is 50 N. If someone could show me the work need to be done to get this answer. Thanks

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Rodiak Rodiak · Answer 1 · 2018-04-13T19:49:42+02:00

Observe the picture.
When object stands on the inclined plane there are four forces acting on it:
1) normal force - perpendicular to plane
2) friction force - opposite to direction of movement
3) gravitational force - perpendicular to Earth's surface
4) force that causes movement - opposite to direction of friction force

We know that block does not move so this means friction force and force that causes movement are same in magnitude. Gravitational force is causing the movement. It is not neither perpendicular or paralel with the surface so we must separate it into component that is paralel and component that is perpendicular to surface.

After calculating we can see that force pulling down the plane:
[tex]m*g*sin \alpha = F_{friction} \\ \\ 100N*sin30=F_{friction} \\ \\ F_{friction} =50N[/tex]

When we have inclined plane we need to separate gravitational force and continue calculations with those components.