Sphere on an incline plane against a wall

[ethan340]

Homework Statement

Find all of the forces acting on the sphere. The problem must be solved in variables. A sphere, mass m, is resting on an incline plane at θ relative to the horizontal. The sphere is also resting against a perpendicular wall relative to the horizontal. Gravity = g.

Homework Equations

f perp. to incline plane= mg(cos θ)
f parallel = mg(sin θ)
fnormal = g

The Attempt at a Solution

Setting up those equations was as far as i got; i still need the force of the sphere against the wall perpendicular to the ground i think

 

[haruspex]

The question ought to state that the surfaces are smooth, otherwise it's indeterminate.
Anyway, your equations are wrong: the first two because they omit any force from the wall; the third because it equates a force to an acceleration, and besides, fnormal is normal to what?
Before writing equations, list and name all the forces that are relevant, stating whatever is known about the directions in which they act and their lines of action. Then choose two directions in which to resolve and write the statics equations.

 

[ethan340]

The question ought to state that the surfaces are smooth, otherwise it's indeterminate.
Anyway, your equations are wrong: the first two because they omit any force from the wall; the third because it equates a force to an acceleration, and besides, fnormal is normal to what?
Before writing equations, list and name all the forces that are relevant, stating whatever is known about the directions in which they act and their lines of action. Then choose two directions in which to resolve and write the statics equations.

haruspex, i appreciate that you've taken the time to read my post and convey what you believe is helpful to me, but unfortunately, your post isn't all that helpful to me. you fail to understand the difference between incorrectness and incompleteness, and the fact that you don't know what i mean by normal force worries me that you aren't qualified to answer this question. by the way, the surface is smooth unless specified otherwise.

in any case, i would like advice on how to solve the problem correctly and understand the methodology behind it.

 

[haruspex]

you fail to understand the difference between incorrectness and incompleteness

If an equation is missing a term it is incorrect.

, and the fact that you don't know what i mean by normal force worries me that you aren't qualified to answer this question.

I know what a normal force is, but it doesn't mean much unless you specify the plane it's normal to. In this case, you already have "f perp. to incline plane", so I guess it's not that. The only other surface of contact is the wall, but normal to the wall would be horizontal.
You have it equal to g (but you probably mean mg), so it sounds like a vertical force.

 

[Nickie]

I would approach this problem by first drawing a free body diagram of the sphere on the incline plane. This will help visualize all the forces acting on the sphere.

From the diagram, we can see that there are four forces acting on the sphere: the force of gravity, the normal force from the incline plane, the frictional force parallel to the incline plane, and the force of the sphere against the wall.

The force of gravity, mg, is acting straight down towards the center of the Earth. The normal force, which is always perpendicular to the surface, will be directed perpendicular to the incline plane and towards the sphere. The frictional force will be directed parallel to the incline plane and in the opposite direction of the sphere's motion.

To find the force of the sphere against the wall, we can use the fact that the sphere is in equilibrium, meaning that the net force acting on it is zero. This means that the sum of all the forces must equal zero. We can set up an equation:

Fnet = mg(sin θ) - mg(cos θ) - Fwall = 0

Solving for Fwall, we get:
Fwall = mg(sin θ) - mg(cos θ)

Therefore, the force of the sphere against the wall is equal to the difference between the force of gravity parallel and perpendicular to the incline plane.

In summary, the forces acting on the sphere are: the force of gravity (mg), the normal force (mg(cos θ)), the frictional force (mg(sin θ)), and the force of the sphere against the wall (mg(sin θ) - mg(cos θ)).