Physics and Graphics Homework

• Determine the resultant velocity:
• Vx = 55 km/h.
• Vy = 25 km/h.
• Vresultant = (55^2 + 25^2)^0.5 = 60.4 km/h.
• α = Arc Tan (25/55) = 24.4 degrees.
• The books must be read:
• Book 1, pages 42-60.
• Book 2, chapter 3.

Homework 2

• Problem 1 from class (see Lecture 2, any questions?).
• Problem 2.3 on page 28 Onouye.
• Determine the force F required to counteract the 600# tension so that the resultant force acts vertically down the pole.
• Use a graphic method to Find F for problem 2.3 on page 28 Onouye.
• Select an appropriate for Step 1 to determine the structures.
• 1" = 200#, so that 600# = 3".
• Use 1:20, each division = 200/20 = 10#'s.
• Per problem statement the resultant has to fall onto the vertical pole.
• Step 2: measure 40 degrees with Horizontal and draw a line.
• Step 3: measure 600#s, that is X = 60 divisions.
• Step 4: Draw a line 40 degrees with the vertical.
• Step 5: Terminate the vector F where it crosses the vertical line.
• Step 6: Measure F with 1:20 which is equal to 710#s.

Homework 3

• Problem 2.3, page 32.
• Determine snow load perpendicular to the rafter acts.
• Using the angle with respect to X: α = arc tan (4/12) = 18.43
• α'= 90-18.43 = 71.57.
• Px = 300*Cos 71.57 = 94.84 lbs.
• Py = 300*Sin 71.57 = 284.61 lbs.
• Use similar triangles.
• Hwk 3.b: Problem 2.11 on page 40 in your text book.
• Select a convenient coordinate system.
• Analytically, for the Resultant to act over the boom, The X component of the weight and force F must balance, that is
• Fx Cos 50 = 200 Cos 60; F = 200[Cos60/Cos50] = 155.57 lb.
• Measurements:
• Select scale 1" = 100 lb.
• Using 1:10 engineering scale, each subdivision is 10 lbs.
• F = 14.4 subdivisions.
• 14.4 subdivisions x 10 lbs/subdivision = 145 lbs which is similar to 155 lbs in the analytical solution.
• Resultant of the weight and force F must fall onto the boom of the crane, therefore stopped its movement at the boom line.
• Complete problem 2.9 on page 40 in the textbook.
• Example: problem 2.11 on page 38 in text book.
• α = tan-1 (8/6) = 53 degrees.
• Since all forces add up to 0 at C: ΣF=0 → ΣFx=0 and ΣFy=0.
• ΣFx=0= -TcaCos53 + TcbCos30 = 0=-0.6Tca + 0.86*Tcb (eqn1).
• ΣFy=0= TcaSin53 + TcbSin30 – 500 = 0 = 0.8Tca + 0.5*Tcb – 500 (eqn2).
• Solving for Tca in eqn 1: Tca (0. 86/0.6) = 1.433Tcb.
• Substituting in eqn 2: 0= 0.8*(1.433*Tcb)+0.5Tcb-500 which equals Tcb=500/1.64=303 N.
• Therefore Tcb=1.433*303 = 434 N.
• Complete Problem 2.11 on page 40 in your text book.

Moment of a Force

• The tendency of a force to produce rotation of a body about some reference point
• Force on a bicycle pedal.
• Weight of fish at the end of a fishing pole.
• Weight on a cantilever structure or canopy.
• The moment of a force is a vector with both magnitude and direction
• The magnitude of a moment of force is calculated with respect to a point A by multiplying the magnitude of force, F, and the perpendicular distance, d, from the reference point A.
• M = F x d.
• The units of force x length = lb-in, lb-ft, kip-in, kip-ft, N-m, KN-m.
• The direction of a moment of force can be clockwise or counterclockwise.
• Read problem 2.14 on page 45 in the textbook.
• Varignon's Theorem: The moment of a force about a point is equal to the algebraic sum of the moments of its components about the same point.

Problem Examples

• Problem 1, Case 1 is a reference.
• Example 2: Problem 2.21 on page 51 in the textbook.
• Problem 2: Complete problem 2.22 on page 51 in textbook.

Homework 4

• Complete problem 2.17 on page 46 in the textbook.
• Complete problem 2.20 on page 51 in the textbook.
• The next class will have a Kahoot on chapter 1 and 3 of the Salvadori book with bonus points for the top three places.

This lesson covers homework problems related to resultant velocity, force calculations, and graphical methods. It includes determining resultant velocity from given components and solving force problems using graphical techniques, focusing on vector representation and measurement.