ENGR1201: Forces in Physics: FBD's

In a couple of weeks, we'll have our first lab. You will need to know how to:

1. Create a "Free Body Diagram"
2. Break forces up into their "x" and "y" components.

Free Body Diagram:
FBD's are diagrams used to show the relative magnitude and direction of all the forces acting on an object in a given situation. All you have to do, is draw arrows for the forces acting on your system.

Example:

In the below picture, arrows showing the forces acting on the two blocks are drawn in.

If there are cables, or supports, the force acts in the same direction as the cable.

Example:

Friction F = u*Fn = (friction coefficient)*(Normal force)
the Normal force = force that is perpendicular to a surface:

Class attendance exercise:
Draw the forces acting on the car, put your name on it, and turn it in at the end of class.

If the force is at an angle, it can be broken up into it's "x" and "y" components:

Below: W is broken up into components that are parallel (W sin theta) and perpendicular to (W Cos (theta) the inclined plane.

Breaking a Force up into "x" and "y" components.
From trig:

triangle showing Opposite, Adjacent and Hypotenuse

"Opposite" is opposite to the angle θ
"Adjacent" is adjacent (next to) to the angle θ
"Hypotenuse" is the long one

Find the length of the sides of the triangle:

http://www.mathwords.com/s/s_assets/s126.gif

Example:

Sine	*soh...*	sin(30°) = 1 / 2 = 0.5
Cosine	*...cah...*	cos(30°) = 1.732 / 2 = 0.866
Tangent	*...toa*	tan(30°) = 1 / 1.732 = 0.577

Class attendance exercise cont:
If the car weighs 2400-lbs:
(a) Solve for the force of gravity acting on the car.

(b) Solve for the normal force (Fn) if the angle of inclination is 30 degrees. (hint, the normal force is the force of the street holding up the car, and is perpendicular to the street. Use a SOH CAH TOA triangle to split up the vertical force of gravity into components that are parallel and perpendicular to the street.)

(c) Solve for the coefficient of friction (u) between the tires of the car and the street. Hint: the friction force = u*Fn.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Class examples cont:
C2) The 600-lb box is held in place on the smooth bed of the dump truck by the rope AB. (Friction between box and truck = 0).
(a) if alpha = 25 degrees, what is the tension in the rope?
(b) If the rope will safely support a tension of 400 lbs, what is the maximum allowable value of alpha?

C3) The weights of the two blocks are W1 = 200lb, and W2 = 50 lb. Neglecting friction, determine the force the man must exert to hold the blocks in place.

C4) A 10-kg painting is suspended by a wire. If Alpha = 25 degrees, what is the tension in the wire?

C5) The masses of the boxes on the left and right are 25 kg and 40 kg respectively. The surfaces are smooth and the boxes are in equilibrium. Determine the tension in the cable and the angle alpha.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

HW #3: Physics worksheet
Put your name, class name, and date on the top of your paper. Use at least half of a page for each problem, include FBD's for each problem, and show all of your work.

Hint: #'s 1, 2, and 3 are just using SOH CAH TOA triangles to find the x (horizontal) and y (vertical) components of the F (hypotenuse).

# 4 & 5 use SOH CAH TOA triangles to solve for "static" forces. "Static" means nothing in the system is moving, because all of the forces balance one another out. If you add the forces in the x direction together, they equal 0, if you add all the forces in the y direction together, they also equal 0.

You can work on this HW in groups, but you each have to turn in your own individual answers.

1. A person exerts a 60 lb force "F" to push a crate onto a truck. What is the value of the horizontal (Fx) and vertical (Fy) components of the force? Hint: Use "SOH CAH TOA", if the hypotenuse of the triangle is "60", and theta is "20", what are the lengths of the other two sides of the triangle?

2. The missile's engine exerts a 260kN force "F". Express "F" in terms of "Fx" and "Fy".

3. A fish exerts a 40N force on the line that is represented by the vector F. Find "Fx" and "Fy".

4. If the coefficient of friction between the car and the street is 0.5, and the car weighs 2000 lbs, what is the maximum angle before the car slips? Hint: start by drawing a FBD of all the forces, orient your coordinate system with the inclined plane, write equations for forces in the x direction, and forces in the y direction, then solve for your unknown.