ME 401 Statics Review Dr. Joseph Vignola Pangborn G43, Phone 202-319-6132, vignola@cua.edu Office Hours: Tuesdays & Thursdays, 1:00-2:00 PM

Working with Vectors and Scalars You need to be very comfortable with vectors. When you are solving problems, be sure you do not mix up vectors and scalars. Make sure you can determine unit vector from pictures. It would be a good idea to review assignment 4 of the Beer and Johnston text book. There are two different ways of determining vectors from pictures. One is the magnitude and directions approach and the other is the component approach. Be able to use both of then. There is a documents on my web page that discusses this and a lot of other helpful issues. Be sure you can work with position, force and moment vectors. http://josephfv.googlepages.com/engr201

Working with Vectors and Scalars Be sure you know how to add, subtract, and multiply with vectors. Multiplication with vectors can mean three different things. Make sure youcan take cross and dot products and that you understand what those products mean physically.

Vector Addition You add vectors by adding the common components

Vector Subtraction You add vectors by adding the common components

Vector Multiplication There are three different way to multiply with vectors First, you can multiply a vector and a scalar The product of a vector and a scalar is a vector

Dot Product The dot product of two vectors is a scalar

Working with Vectors and Scalars You will need to be able to take cross products to find moment vectors The moment of a force about a point is

Drawing Vectors From Pictures We have two approaches Component approach Sometime the drawing will tell you “how much” of the vector is aligned along each of the coordinate axes. For example: given a picture like this we can use simple trig to find the components

Drawing Vectors From Pictures We have two approaches Magnitude – direction all vectors can be written as , where is the magnitude and is a unit vector and tells us the direction. Sometime the picture tells you how “long” the vector is (the magnitude) and gives you some indication of direction.

Drawing Vectors From Pictures We have two approaches The vector is contained in the plane OBAC. Resolve into horizontal and vertical components. Resolve into rectangular components

Drawing Vectors From Pictures Finding the unit vectors with the cosine approach. This involves projecting the vector to the coordinate axes. The projection is of a unit vector on to an axis is just the cosign of the angle between the axis and the unit vector. The trouble with this is that only in a few of the problems do we know the angle between the coordinate axes and the vector you’re taking apart. But if you know some or all or the angles you can write the unit vector as:

Diagrams and FBDs Free-Body Diagram: A sketch showing only the forces on the selected particle. Space Diagram: A sketch showing the physical conditions of the problem.

Free Body Diagrams A free body diagram is a simplified picture that emphasizes the vector quantities in the problem. In my document on the web page you can find many example problems to try. Be sure that you can draw free body diagrams for systems made of a single rigid body. Additionally, be ready to draw multiple free body diagrams for systems make up of a number of rigid bodies like those in chapter 6 of the Beer and Johnston book. Make sure you label the forces and moments in your free body diagram, and remember that you can have both scalars and vectors in a free body diagram so make sure the distinction is clear.

Reactions The reactions that you need to include in the FBD Ask yourself “what motion is prevented?”

The Five Step Method Step 1. Draw a Free Body Diagram (FBD) Step 2. Write out the force and moment vectors Step 3. Sum force vectors Step 4. Sum moment vector Step 5. Solve system of equations   This approach always works, no exceptions.

The Five Step Method Free body diagram

The Five Step Method

The Five Step Method

The Five Step Method

The Five Step Method

Example Problem 4.4

Example Problem 4.4

Example Problem 6.4

Example Problem 6.4