Physics Free Body Diagram Question.?

Question

A spherical mass rests upon two wedges. The sphere and the wedges are at rest and stay at rest. There is friction between the sphere and the wedges. Draw a free body diagram for the spherical mass.

I know the force of gravity would be going down, I just don't know how the normal and friction forces would go. Help please??

Answer 1

Normal force is always perpendicular to a surface (that's actually what "normal" means in geometry).

Friction is always along the surface.



So for a horizontal plane the normal force is vertical and friction is horizontal; for a plane tilted 20 degrees from horizontal, the normal force is 20 degrees from vertical and friction is 20 degrees from horizontal.



You didn't ask about the forces on the wedges, but note that they each exert a net horizontal force on the sphere (the forces from the two wedges balance each other). This means the sphere exerts a net force on each of them. There needs to be a force such as friction keeping the wedges from sliding apart.

Answer 2

Newton's third law of motion states that for every action there is an equal and opposite reaction. That it why you don't fall through your chair when you sit. Because the chair is pushing back on you with the same amount of force that gravity is pushing you onto the chair. If the force of gravity is greater on you is greater that the maximum force that the chair can put out then you fall through the chair because the amount of newtons going down is greater than the amount of newtons pushing you up causing you to go down. The same thing applies here. As the force of gravity is pushing down on the sphere the net force of the two wedges pushing up on the sphere equal that of gravity pushing down so that the forces are balanced and the sphere does not move. Look at the picture for an example. I don't actually know how much force is coming down on the sphere.

Answer 3

The sphere is supported by:

- the left wedge (contact point L)

- the right wedge (contact point R)



O

L R



Draw the sphere. (Don't draw the wedges.)



There are 5 forces to mark on the sphere



1) It's weight, vertically downwards passing through the centre of the sphere ↓



2) The normal contact force from the left wedge; this passes through L and points radially inwards ↗



3) The normal contact force from the right wedge; this passes through R and points radially inwards ↖



4) The frictional force of the left wedge on the sphere; this acts through L and is a tangent to the sphere pointing outwards ↖



5) The frictional force of the right wedge on the sphere; this acts through R and is a tangent to the sphere pointing outwards ↗

Answer 4

It has been my experience that FB diagram rules may vary slightly depending on text, teacher, institution, etc.



I was taught that the FB diagram should show ONLY the single object being examined, and ONLY the forces that act ON it. Following this idea, U would NOT show BOTH normal force/s AND force of gravity as these would be equal and opposite forces, and only the Normal force/s act ON the sphere. U would show a diagram of the sphere (mass), and two upward NORMAL forces representing the two forces of the wedges against the sphere. {If the wedges are deemed equal in size and shape and relative position then the forces each creates is 1/2 the weight(mg) of the sphere} The two STATIC forces of friction would be shown acting HORIZONTALLY on the sphere at the same two points along the bottom of sphere that the wedge forces act. As U don't know (left or right) which way the sphere would roll off of the wedges if there were no friction forces acting, it might be a good idea to show one friction force acting to the right on sphere and the other horizontal friction force acting to the left.