10/28/09 Class

We spent the majority of class time today going over HW 4F and the concepts covered by said homework assignment. Problem 1a involves drawing a free body diagram for a 40 kg chest sitting on a 20° ramp with a man pulling on a rope attached to the chest at a 30° angle. The question asks you to solve for the minimum tension force the man must exert on the chest to keep the chest from moving (this problem disregards friction) using a graphical method. First you should solve for the only force you know at first: the gravitational force. Using the equation

, you can calculate the downward gravitational force to be about 400 N by calculating . Once you draw this into your FBD, you should be able to see

another fact; both the normal force and the tension force have to act in set directions. The normal force acts perpendicular to the surface while the tension force acts at 30° to the surface. Because the chest is not accelerating (or moving for that matter), the net force must be zero and when the vectors are drawn tip-to-tail when you add them up, they should form a loop. Therefore, you can draw lines along the points where the vectors should pass through (for example, the tension force vector must pass through the tail of the gravitational force vector). Once you have done this, you can see the length's of the normal and tension force vectors. Now you simply need to measure the length of the tension force vector and use your scale to find the approximate magnitude of the force (it should turn out to be about 150 N). The following shows what your finished vector drawing should look like:

For problem 1b, you are supposed to solve the problem using the component method. The three sets of components are , , and (these could be derived by using sin, cos, tan trigonometry). Knowing that the net force is zero, you can add up all the x-components and all the y-components and both sums will be zero. Knowing this and after solving the equations for the tension force, the tension force turns out to be about 158 N (very close to the graphically found answer from 1a).

This is what we did in class today. Next scribe is Jason.