1. ME 401 Statics Review Dr. Joseph Vignola
Pangborn G43, Phone ,
Office Hours: Tuesdays & Thursdays, 1:00-2:00 PM

2. 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.

3. 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.

4. Vector Addition
You add vectors by adding the common components

5. Vector Subtraction
You add vectors by adding the common components

6. 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

7. Dot Product
The dot product of two vectors is a scalar

8. 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

9. 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

10. 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.

11. 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

12. 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:

13. 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.

14. 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.

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

16. 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.

17. The Five Step Method
Free body diagram

18. The Five Step Method

19. The Five Step Method

20. The Five Step Method

21. The Five Step Method

22. Example Problem 4.4

23. Example Problem 4.4

24. Example Problem 6.4

25. Example Problem 6.4