23.3 APPLICATIONS OF FRICTION

---

À  p

When dealing with these problems the direction of friction forces must be assigned with care. If the directions are selected backwards, the solutions will be incorrect.

Before assigning friction forces the impending motion should be analyzed. To do this think of the possible cases that might cause the bodies to start moving - do not assume that all friction surfaces must go into motion. At times this approach may mean that multiple solutions will have to be done to solve a problem.

The general methods to be followed in these problems involves,

1. Examine the problem to determine impending motion for each individual object, and the overall system. There may be one or more possible cases, each will require a separate solution.

2. Based upon the assumed motion at the points of contact, drawn on friction forces that oppose the motion. Also draw on normal forces.

3. Solve the problem using normal statics (but avoid using sums of moments for friction forces when they don't act on a clear point).

4. Examine the solution (and compare to others) for anomalies such as normal forces that separate friction surfaces. This will help determine problems, and to eliminate unreasonable solutions.

23.3.1 Wedges

(|

Wedges are a useful engineering tool, and the approach used for wedges also finds its way into other engineering applications.

A good rule to stick to is that when a wedge is in use, the forces on the faces will both be in the same direction. That is either towards, or away from the point of the wedge.

When solving friction problems we look for friction that is about to let go and start slipping. Keep in mind that not all surfaces will slip, this should be verified after the solution. For all surfaces that slip the friction force will be at the maximum value.

The example below shows how to deal with a multiple wedge problem. ([Hibbeler, 1992], prob 8-55, pg. )

[working model file]

Consider the problem below,

****************** Solve using Mathcad *******************

23.3.1.1 - Practice Problems

´ð´0

1. The angled bar below has two forces applied that are tending to push it in a counterclockwise direction. These forces are resisted by a wedge that is kept in place by friction (the coefficient of friction is 0.20). determine the force P that is required to pull the block out.

[working model file]

2. We are designing a firing mechanism for a new gun that uses two identical rails that are pressed together to accelerate a projectile. In the figure below we see the two rails at an angle before firing begins. When firing begins, the force `F' will be applied, overcoming the coefficient of friction of 0.05. The length of the projectile is negligible, but it has a wedge shape that matches the rails before firing. What is the initial force `F' that must be applied to the rails before the shot begins to move?

3. What force P will have to be applied to the wedge A to force the blocks B and C apart? You can assume that the coefficient of friction is 0.4 at all points of contact.

4. Find the force required to pull out the wedge below.

5. Find the force required to pull out the wedge below.

23.3.1.2 - References

´ð´0

Hibbeler, R.C., Engineering Mechanics: Statics and Dynamics, 6th edition, MacMillan Publishing Co., New York, USA, 1992.

23.3.2 Belt Friction

(|

Belts are a common tool for transmission of forces, motions and velocities.

If we have a flat belt, it primarily depends on friction to hold it in place.

The basic rules of static friction still apply for local friction between the belt and the drum, but over the length of the belt the effective normal force changes.

If we consider one element of the belt we can see an element of friction and a differential of tension.

An example of belt friction is given below (8.123, pg. 40, Beer and Johnston). In this problem the upper drum is moving slowly (this means the belt sticks with static friction), the lower drum allows the belt to slide (the belt slides with dynamic friction). We need to find the force W that will balance the 150lb load on the other side.

Consider the simple problem below,

V-belts use the same principle as flat belts, except the friction is increased by the angle of the sides.

23.3.2.1 - Practice Problems

´ð´0

23.3.2.2 - References

´ð´0

Beer, F.P., Johnson, E.R., Statics & Mechanics of Materials, McGraw-Hill, 1992.

Soustas-Little, R.W. and Inman, D.J., Engineering Mechanics Statics, Prentice-Hall, 1997.