Learning Module 5: Forces in a PlaneHomeworkShow how to resolve a force into perpendicular coordinates1. Let F be a vector with magnitude 5 pointing 10 degrees above the positive x-axis. Let G be a vector with magnitude 14pointing 40 degrees above the positive x-axis. (These are the same F and G from LM2.) Express each of F and G inCartesian form. (F = something * i + something * j).2. In your text, work problem 2.24 (pg. 33).Show how to find a force component along a line (by geometry and by vector algebra)3. In your text, work problem 2.25 (pg. 33).4. The bolt goes into the roof along the n-axis. P is 150 lbs. Any force perpendicular to the n-axis (that is, any force along theline of the roof) tends to shear off the bolt. Using vector methods, find the component of P along the line of the roof.5. Resolve the force F2 into components acting along the u and v axes and determine the magnitudes of the components.1/14/2009MAE206 Forces in a Plane Homework…ncsu.edu/…/lm5_homework.html?pa… 1/3Hint #1: u and v are not perpendicular.Hint #2: draw triangles with all the angles labeled.Hint #3: F needs to equal Fu plus Fv.Hint #4: Use the parallelogram law.Hint #5: Use the law of sines.Show how to add forces6. In your text, work problem 2.35 (pg. 34).7. In your text, work problem 2.42 (pg. 35).Show how to write a force as a scaler times a unit vector8. Consider the three forces shown below (from your LM2 homework set where alpha = 120 degrees). Consider that the y-axis points up the page and the x-axis points at your right hand. Write these vectors in terms of scalars times the appropriateunit vector.Find the angle between two forces (by geometry and by vector algebra)9. Consider the vectors F and G from number 1 above. For each of the following, write out the formulas you would use andthen find the values requested. (Getting the right answer is only half the problem. Please show your work.) a. Find the resultant R = F + G. b. Use the Pythagorean Theorem to find the magnitude of F + G. c. Use the tangent function (from trig) to find the angle between R and the x-axis. d. The cosine of the angle between two vectors is equal to the dot product of their unit vectors. Find the angle between Fand R. e. Is your answer for d the same as your answer for c minus 10?Show how to find a position vector and how to specify a force using a position vector10. Find the unit vector e in the figure below that is directed from point A to point B. Also, express the force vector F interms of its x and y components. Let F = 15 N. 1/14/2009MAE206 Forces in a Plane Homework…ncsu.edu/…/lm5_homework.html?pa… 2/311. In your text, work problem 2.29 (pg. 34).1/14/2009MAE206 Forces in a Plane Homework…ncsu.edu/…/lm5_homework.html?pa…
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