Block on a Plane Ex from Morin-Statics

[veezbo]

Homework Statement

Example (Block on a plane): A block of mass M rests on a fixed plane inclined
at angle theta. You apply a horizontal force of Mg on the block, as shown in figure 1-1 (attached). The free-body diagram for this is also attached as an image.

Assume that the friction force between the block and the plane is large enough
to keep the block at rest. What are the normal and friction forces (call them N
and F_f) that the plane exerts on the block?

Homework Equations

Just the use of basic statics?
Also trigonometric expressions involving sin and cos

The Attempt at a Solution

I initially try to find F_f itself by drawing the vector connection the heads of F_f and the Mg applied force (as shown in the free-body diagram).
However, I cannot find F_f this way.
I think there is something I am missing while trying to balance the forces.

 

[hikaru1221]

Write down the vector equation for forces in equilibrium $$\Sigma \vec{F} = 0$$, and solve it

 

[veezbo]

Thanks Hikaru! I had never actually heard of statics before, and my book (Morin) was not very clear on how this worked.

But I think I finally figured out how it works.

I have another question though: since F_f = Mg * sin(theta) - Mg * cos(theta), shouldn't this imply that the magnitude of F_f is that same expression?
If so, then I feel like there should also be a geometric solution.

 

[hikaru1221]

I also agree that Morin's book isn't so instructive and therefore not appropriate at introductory level, though insightful. It requires the readers to know quite a lot before reading it.

Yes, you got the correct answer This lies behind one equation: $$\Sigma \vec{F} = 0$$, which can be viewed under either geometric angle or algebraic approach.

 

[rwisz]

Thank you for sharing your problem with us. In order to solve this problem, we need to consider the forces acting on the block and the plane. The forces acting on the block are the gravitational force (Mg) and the friction force (F_f). The force acting on the plane is the normal force (N). Since the block is at rest, the sum of all the forces acting on it must be equal to zero.

To find the normal and friction forces, we can use basic statics principles. First, we need to draw a free-body diagram of the block, with all the forces acting on it labeled. Then, we can use trigonometric expressions involving sin and cos to determine the magnitudes of the forces.

In this case, the normal force (N) is equal to the component of the gravitational force (Mg) perpendicular to the plane, which can be calculated using the angle theta. The friction force (F_f) is equal to the component of the gravitational force parallel to the plane, which can also be calculated using the angle theta.

Remember to always consider the direction of the forces when solving statics problems. In this case, the normal force is pointing perpendicular to the plane, while the friction force is pointing in the opposite direction of the applied force.

I hope this helps you solve the problem. If you need further assistance, please don't hesitate to ask for clarification. Keep up the good work!