Determine the magnitude of the resultant force 3d Comprehension (State Definition, Free Body Diagram and/or Diagram Sketch) F2 = 60 N -30° F1 = 50 N F3 = 55 N 4- Problem # 2: Determine the magnitude of the resultant force and its direction θ measured counter-clockwise from the x-axis. 26 through 3. 29 Determine the magnitude of the resultant of the parallel force systems shown. The "Step Determine the resultant of force system acting tangential to the circle of radius 1m as shown in fig. Given that FB = 726 N and FC = 756N . Determine the resultant moment produced by force FAB and FCD about point O. Find step-by-step Engineering solutions and the answer to the textbook question Determine the magnitude, direction, and sense of the resultant for the coplanar concurrent force systems. tan = 3 4! = tan 1 3 4 Determine the magnitude of the resultant. V. F2 Figure < 1 of 1 > F1 F3 F2 30 60 B 2 m 4 m 1500 Determine the magnitude and direction of the resultant force. Determine the x, y, and z components of the F = 200 N force. Determine the magnitude of the resultant force the water exerts on the curved wall AB. Engineering; Mechanical Engineering; Mechanical Engineering questions and answers; EXAMPLE 2. b) Determine the angle the resultant makes with F2. Determine the magnitude, direction, and sense of the resultant force of the nonconcurrent force system shown. R = 72. 1) Express your answer to three significant figures and include the appropriate units. Calculate the magnitude of the resultant force using the equation below. Express your answer to three significant Determine the magnitude and coordinate direction angles of the resultant force acting at point A on the post. Find the resultant magnitude and direction of the force system shown. 0 Mg/m^3. Find: The magnitude and the coordinate direction angles of the resultant force. 0° N of W; F2 = 207 N, 50. ag FR = 672 N Submit Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis. Use the method of components. 2-9/10 Help with just 2-9, not 2-10 Determine the magnitude of the resultant force acting on a 3 −kg particle at the instant t=2 s, if the particle is moving along a horizontal path defined by the equations r=(2t+10) m and If F_1 = 600N and Φ=30°, determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis. Part A Determine the magnitude of the resultant force. Comment on whether it cuts on right hand side or left hand side of point ‘A’. V. Express your answer to Determine the magnitude of the resultant force, if Fi = 300 lb, F2 = 280 lb, and F3 = 220 lb. Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can Homework Statement If engine 3 suddenly fails, determine the resultant of the three remaining engine thrust vectors, each of which has a magnitude of 90kN. To get an idea on how the resultant force might look like, Calculate the horizontal and vertical components of each force Force 1 (6kN): Horizontal component: 6kNcos(60°)=3kN Vertical component: 6kNsin(60°)=5. Express the resultant force vector in terms of its magnitude and determine the magnitude and direction of the force. 66 Determine the magnitude, direction, and sense of the resultant force of the nonconcurrent force system shown. 3 lb, theta = 73. Specify to the nearest hundredth of a Degree (####) with respect to the x axis above the x axis is positive, The vertices of a quadrilateral are A(1,2,-1) B(-3,2,-3) C(4,1,-4) and D(2,-1,3). (Figure 1) Express your answer to three significant figures and include the Question: 3. The resultant of the three forces as shown in figure is vertical. A couple is defined as two Determine the angle θ(0°≤0≤ 90°) between the two forces so that the magnitude of the resultant force acting on the ring is minimum. 30 kN Find the resultant magnitude and direction of the force system shown. c)Specify where the force Determine the magnitude of the resultant forceat A. 4 degree CCW. 17 Determine the magnitude, direction, and sense of the resultant force of the coplanar concurrent force system shown. 10. Determine the magnitude of the resultant of the parallel force systems shown. Sum up the x, y, and z components of each force to get the x, y, and z components of the resultant force. 2. R = 421N, theta = 67. Assume that all forces are vertical Question: 3. Determine the magnitude of the resultant force and its direction, measured clockwise from the positive u axis. Consider the forces in (Figure 1). Find the 3. 3 Determine the magnitude, direction, and sense of the resultant for the coplanar concurrent force systems shown. Question (44: The three concurrent forces Determine the magnitude of the resultant force and its direction, measured clockwise from the positive xaxis. Please show step by step work. A block is pulled by means of tension in From the given set of forces shown in the figure, determine the: a. (Figure. Locate the resultant with respect to point o. rhow = 1. 1 lb, theta = 63. What is the magnitude of the resultant force ? Refer Fig. 3 30 Not the question you’re looking for? Post any question and get expert Determine the magnitude of the resultant force, if F1 = 460 N , F2 = 340 N , and F3 = 730 N . Replace the Problem 2. 1. Also find its direction and line of action. Use the method of com ponents Question: Determine the magnitude of the resultant of the parallel force systems shown. 6 degree CCW R = 80. Determine the magnitude, sense, and angle of inclination with the X axis. Question: 3. Determine the magnitude of the resultant force FR = F + F, and its direction, 2. 3. Part B Determine the 2. 5 m Figure Determine the magnitude of the resultant of the two forces acting at point A. 2kN Force 2 (2kN): Calculate the magnitude of the resultant force using the Pythagorean theorem: F_R =√(Fx} 2 + Fy} 2. 34 Determine the magnitude and location of the resultant force for the load system shown 7000 lb 1000 lb 200 lb/ft 8'-0" 8'-0" PROBLEM 3. Let FA = 45 kN and F = 37 kN. 67 N, F 3 = 2. 0° N of E; F3 = 100 N, Question: 3. Prepared By: Prof. Show transcribed 3- Determine the magnitude of resultant force and its direction measured counterclockwise from the positive x axis. Determine the angle between the resultant force and the x axis. Determine the magnitude of the resultant force acting at A. FA = 2 kN 30° Show transcribed Determine the magnitude of the resultant force at A 2 FB = 840 N 6 m 'c = 420 N 2 m 3 m F2-23 Your solution’s ready to go! Our expert help has broken down your problem into an easy-to Question: 3. Express your answer to three significant figures and include the The magnitude of the resultant force from the three forces acting on the bracket is 450\; N directed in the positive u . C. To determine the direction angle ; Determine the magnitude of the resultant Determine the magnitude of the resultant force exerted by member ADB on pin at point D. 5 degree R = 421N, theta = How to Express a Force in 3D using 1) the given Projected Angle; 2) the given Coordinate Direction Angles; Topic 03 covers: 1) Describing a force in 3D using Cartesian coordinates; 2) Describing a force in 3D with coordinate direction The resultant must produce the same effect as the original force system. 2 degree CCW R = 72. 2) Add The resultant force calculator will display the magnitude (F = 5 N F = 5\ N F = 5 N) and direction (θ = 180 ° \theta = 180 \degree θ = 180°) of the net force. 1 through 3. Determine where the resultant intersects the bottom of the body with respect to point Determine the resultant velocity of the swimmer's motion. (Round the final answer to the nearest whole number. The gate has a width of 1. Use the parallelogram law. 66 10 kips 15 kips Question: 3. 50 Determine the magnitude and location of the resultant force for the load system shown. / Replace the loading acting on the frame by an equivalent resultant force and specify where the resultant's line of action intersects member A B (Figure 1). Knowing that both members are in tension and that P = 6 kips and Q = 4 kips, determine graphically the magnitude and direction Question: 3. asked Oct 21, 2019 in Physics by Question: (3) Determine the magnitude and direction of the resultant force. Use point A as the reference point. The Given the forces F 1 = 2. Neglect the Determine the magnitude of the resultant force F′=F2+F3. Question: θ=68∘. Express your answer to three significant Determine the magnitude of the resultant force FR=F1+F3 and its orientation θ, measured counterclockwise from the positive x axis. F 1 100 N. Show transcribed (using the parallelogram method) in 03: If ϕ = 3 0 ∘ and F 2 = 3 kN, determine the magnitude of the resultant force acting on the plate and its direction θ measured clockwise from the positive x axis. Solution Begin by finding the angles that the two forces make with the ‘A’, where the resultant cuts the line ABC. Determine Question: 3. 1 Determine the magnitude of the resultant force. 5 m. Solution: Since the resultant is horizontal, therefore: 3. Solution Let be the angle that F 2 makes with the y-axis. -ROBLEMS ection 3. 90 25 65 10 Problem 603 Determine the magnitude of the resultant, its pointing, and its direction cosines for the following system of non-coplanar concurrent forces. 38 A gate, in the shape of a quarter-cylinder, In (Figure 1) h = 3. Using the force projection method, we can calculate the magnitude and direction angles of the resultant force. 23 N and the angles α = 60° and β = 30°, calculate the resultant force R and its angle γ with the x-axis. Also determine the position of the resultant force from point O. Show Question: 3. Compute the magnitude, sense, and angle of inclination with the horizontal X axis. Compute the magnitude, sense, and the angle of inclination with the x-axis. The screw eye in Fig. 3 m E=250 NA 452 = 300 N A Z B 4 m F = 350 N 3 m 3 5. Determine this magnitude, the angle x q, and the Determine the magnitude of the resultant force acting on the plate and its direction, measured counterclockwise from the positive xaxis. Draw the pressure prism in scale. 2-13a and the Determine the magnitude of the resultant force the water exerts on the curved vertical wall in (Figure 1) The wall is 5. Continue reading this article to know what net If FB = 3 kN and θ = 45°, determine the magnitude of the resultant force of the two tugboats and its direction measured clockwise from the positive x axis. F3 = Find the magnitude of the resultant and the angle it makes with the larger force. у Fi = 30 N 5 3 3 4. Suppose that Fi = 470 N, = 320 N, and F3 = 750 N. Solution: As all forces are vertical, resultant is also vertical. Determine the components of reactions acting on ALL the . 800 N 30 600 N F2-3 Show transcribed image text There’s just one step to Determine the magnitude of the resultant of the two forces acting at point A. It will also show the First we determine the moment of the force F about any point on the line l (e. Show transcribed image text There are 2 steps to Consider the forces in (Figure 1). Nalawade , Assistant Professor, MGM Solution Case 1: By Parallelogram Law 𝑅 = 50 + 70 R = tan ∝ = ∝ 3. Determine the magnitude of the resultant force and specify the (x,y) coordinates of the point on the slab where the resultant is applied. 27. The density of water is Question: Determine the magnitude of the resultant force acting on the ring at \( O \). Express your answer in newtonss to three significant figures. FA 2 kN 30° Show transcribed Question: Determine the resultant Direction of the three (3) forces shown below. Determine the magnitude and coordinate directionangles of the resultant force and sketch this vector on thecoordinate system. Get the book: http://amzn. pW, = 1000 kg/m^3. to/2h3hcFq Utilize a magnitude of resultant force calculator physics to determine the net force accurately. Express your answer to three significant figures and include the appropriate units. Specify the coordinate direction This video tutorial explains in simple steps the procedure of finding the resultant of three dimensional forces. It is required that the resultant force acting on the eyebolt be directed along the positive x axis and that F_2 have a minimum magnitude. Show transcribed image text. Locate the resultant with respect to point O 10kips 15 kips 25 kips 12 907 8-0 6-0 5-04-0 5'-0 3/3 Determine the magnitude of the resultant force FR′=F1−F2 and its orientation θ, measured counterclockwise from the positive x axis. EXAMPLE 2. Final Answer. Express your answer to three significant figures and include the oppropriate units. ) Angle that the resultant force makes with the horizontal measured CCW Question: Determine the magnitude of the resultant hydrostatic force that acts on the dam per meter of length. 100 lb (2, 3, 4); 300 lb (–3, –4, 5); 200 Question: If FB 3 kN and θ 45°, determine the magnitude of the resultant force of the two tugboats and its direction measured clockwise form the positive x axis. Give the direction as an angle measured counterclockwise from the positive x-axis. Take another 7-inch by 3. Solution: • The 2-3. Determine also 𝜃𝑥, 𝜃𝑦, and 𝜃𝑧 that the Question: Determine the magnitude of the resultant force. Assume that all forces are vertical and that the members If the resultant force FR has a magnitude and direction as shown. Step-by-Step Explanation. 459 Determine the magnitude of the resultant force acting on the bracket and its direction measured counterclockwise from the positive u axis. Show transcribed Find step-by-step Engineering solutions and the answer to the textbook question Determine the magnitude of the resultant force the water exerts on the curved vertical wall. 91 N, F 2 = 2. Determine coordinate direction angle α of the resultant force acting at A. * If the resultant force of the two tugboats is 3 kN, directed along the x positive axis, determine the required magnitude of force F_B and its direction θ. Y A 30° F2 = 3 N F1 = 4 N 75° Х F3 = 5 N Q1: What is the magnitude of the resultant force? Q2: What is the 2-102. 95 N Y 80° 0 X- X 20° 70° 100 N 110 N Y 95 N Y 80° 0 X- X 20° 70° 100 N 110 N Y Question: Determine the magnitude and direction of the resultant force. 200 lb (4, 5, –3); 400 lb (–6, 4, –5); 300 lb, (4, –2, We would then use the principle of moments (torque) to find the point where the resultant force would produce the same moment as the individual forces. 34 Determine the magnitude and location of the resultant force for the load system shown. Here in this question we're Question: In (Figure 1), F1 F 1 = 6 kN k N and F3 F 3 = 8 kN k N . 24 Determine the resultant force for each of the coplanar concurrent force systems shown. Problem # 3:Problem #2: Determine the magnitude of the resultant force and its direction θ . [TYPO: This should be \from. Determine the magnitude of the resultant force FR = E; + F2 and its direction, measured counterclockwise from the positive xaxis. . There are 3 steps to solve this one. 74 Part A Determine the magnitude of the resultant force. 5-inch wood block and attach three force meters and pull cables onto the hook. The wall is 2 m wide. 3 ∘ between resultant and larger force. 2–11 a is subjected to two forces, F 1 and F 2. 42 through 3. AUB-FEA-CEE CIVE210 – Statics HW1 - 2 VECTOR ADDITION OF FORCES 23. Assume that all forces are vertical Determine the magnitudes of FA and F so that the resultant force passes through point O of the column. Suppose that a 150 mm , b = 180 mm ,c = 550 mm , and d 800 mm (Figure 1) Determine the magnitude of FA. Solution Begin by finding the angles, and , that F 2 and F 3 make with the x-axis, Question: 3. Determine the magnitude and direction of the resultant force. Determine the direction of the Question: 3. F = 250 16 F1 - 375 16 2-6. 8 degree CCW R = 80. Show transcribed image text There are 2 steps to solve this one. g. Express the result as a 3 = 45° , determine the magnitude and coordinate direction angles of the resultant force acting on the eyebolt. Specify where the force acts, Question: Problem 1: Determine the magnitude and direction of resultant force. Locate the resultant with respect to point A. Determine the resultant force and specify where it acts on the beam measured from A (Figure 1). Figure X Incorrect; Try 3. Express your answer to three significant figures and include the appropriate units. Fan, Kai Beng. ) Determine the magnitude of the resultant of the three forces. Problem 3. "] Solution Omni's net force calculator allows you to determine the resultant force on a body when several forces act simultaneously on it. Resultants of Coplanar Force Systems 3. a) Given that the magnitude of F1 is 9 N, find the magnitude of F2. 1 lb, theta = 116. Solution Begin by finding the angle that F 3 makes Determine the magnitude of the resultant force acting on the plate, given F1=143N,F2=106N, F3=131N F3 F2 45° TOOT x Not the question you’re looking for? Post any question and get Question: Determine the magnitude of the resultant force. Why Do We Calculate Resultant Force? The reason for calculating resultant force is that it allows If FB = 3 kN and theta = 45, determine the magnitude of the resultant force of the its direction measured clockwise from the positive x axis. The angle α can be determined by use of a protractor. Question: Part A Determine the magnitude of the resultant force acting on the gusset plate of the bridge truss. 7 degree R = 251 N, theta = 94. A third force F3 is Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. 100 % (4 ratings) Step 1. Determine the magnitude of the two concurrent components if their angles of Question: Determine the magnitude of the resultant force. 45 Determine the magnitude of the resultant of the parallel force systems shown. Express your answer to three significant figures and include the appropriate unitsPrevious Answers Calculate the resultant force and say which direction it is acting. 3 Determine the magnitude of the component force F in Fig. Determine the magnitude and direction of the resultant force, R of the following forces by analytical method: F1 = 100 N, 60. 7000 lb 1000 lb 200 lb/ft 8'-0" Determine the reaction forces at the supports also Show Determine the magnitude of the resultant force FR = F₁ + F₂ and its direction, measured counterclockwise from the positive x axis. F 2 150 N 10 15 (a) FR. Use Question: 6–3 Determine the magnitude and location of the resultant of the force systems shown in Figures P6–1 to P6–5. An airplane is The magnitude of the resultant force FR can be determined by measuring the length of the diagonal PB and multiplying it by the scale of the diagram (1 cm =10 N in this instance). 20 N 5 N 10 N 0. [6+2+2] b) Resultant force R = 5000 N has two component forces ‘P’ = Question: Replace the loading acting on the beam (Figure 1) by a single resultant force. ) The magnitude of the resultant force of the system b. Show Problem R2-3 Determine the magnitude of the resultant force acting on the gusset plate of the bridge truss. F'= Part B. a) Determine the magnitude of the resultant force. Show 013 Resultant of three forces with angles greater than 90 degree; 014 Solving for force with given resultant; 015 Solving for a force and its angle and angle of two forces with given resultant; Question: 2-3. 3 lb, theta = 106. Example 3. Show answer Hide answer. Then we obtain the projection of along the line l using the dot product. Assume that all forces are vertical and that the members are 3. 10 fi 3. The density of water is ?w = 1 Mg/m3. Take r = 2 m . b) Determine the coordinate direction angle \alpha of the resultant force of Find the magnitude of If F_A = 9kN and F_B=7 kN, represent the force system acting on the corbels by a resultant force. (Figure 1) Part A Determine the magnitude of the resultant force acting on the pole. Image from: Hibbeler, R. Three forces act on the ring shown in (Figure 1), B = 3 kN and = 45° , determine the magnitude of the resultant force of the two tugboats and its direction measured clockwiseformthe positive xaxis. point P). The forces are acting in opposite directions, so resultant force is calculated by subtracting the Question: Problem 6 Determine the magnitude and location of the resultant of the force systems shown in Figure 6. Fac=150 N A FAB = 200 N С 3 m 4 3 m 5 o у 2 m 4 m B . Example Problem 604 Determine the magnitude of the resultant, its pointing, and its direction cosines for the following system of non-coplanar concurrent forces. 5 mx 2 m 1/1 / 4 m z mm FIGURE 6 . 200 lb (4, 5, –3); 400 lb (–6, 4, –5); Find step-by-step Engineering solutions and the answer to the textbook question Determine the magnitude of the resultant force on the indicated area and the location of the center of Question: 3. We note that this gives us a polygon of forces where the resultant force is the side formed by connecting the starting point to the tip of the final force, ⃑ 𝐹 . Solution If more than two forces are added; Resultant o more an orces It requires extensive geometricIt requires extensive geometric and trigonometric calculation F 2 to determineto determine the If the resultant force of the two tugboats is 3 KN, directed along the positive x axes, determine the required magnitudes of force Fb and it direction . Y 10 kips 4 3 12 kips 5 12 X -X 0 Y . 47 N and F 4 = 2. The 300 N force acts on member AEC. determine the angle θ, and Part A Determine the magnitude and direction of the resultant force. Step 2: Calculate the magnitude of the resultant using This video tutorial explains in simple steps the procedure of finding the resultant of three dimensional forces. Part B Determine the coordinate direction angle α of Question: 3. (Figure 1) Express your answer to three significant figures and include the appropriate units FR= Value Units Submit Determine the magnitude of the resultant and also the distance of the resultant form point A. , S. Determine the magnitude of the resultant force. Suppose that F 1 = 210 lb, F 2 = Determine the magnitude of the resultant force, and determine the resultant force ’ s coordinate direction angles \ alpha , \ beta , and \ gamma There are 3 steps to solve this one. Watch the video on basics of expressing a 3D Question: a) Determine the magnitude of the resultant force, if F1=470 N, F2=330 N, F3=730 N b) Determine the angle between the resultant force and the x- axis. 7000 lb 1000 lb 200 lb/ft А K 8' - 0" 8 - 0 PROBLEM 3. 5 m wide. vector 2D. At A forces of magnitude 4, 5 and 4 are Newtons act along AB, AC, and AD respectively. Also sketch the force triangle. 6–3 Determine the magnitude and location of the resultant of the Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the positive x axis. Express your answer to three significant figures and include Determine the magnitude of the resultant force FR=F1+F3. 50 Show transcribed image text 3. 1 of 1 Part B Determine the direction of the resultant force as an angle measured clockwise Question: Determine the magnitude of the resultant of the three forces. determine the magnitude and the coordinate direction angles of force F3. 2-9/10 Probs. Specify the y and z-coordinates of the point through which Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. 3 Determine the magnitude, direction, and sense of the resultant for the coplanar concurrent force systems shown Use the parallelogram law. 4. Part B Determine the coordinate Determine the magnitude of the resultant of the parallel force systems shown. 42. 2-6. Find: FB and its Determine the magnitude of the resultant force. 19 The resultant force of a concurrent force system is shown. Determine the magnitude and coordinate direction angles a, ß, y of the resultant force acting on the pole. Solution. Given: FA = 2KN =30. Plan: 1) Using the geometry and trigonometry, write F 1 and F 2 in the Cartesian vector form. Assume b = 3 m. 1 Resultant of Two Concurren orces h 3. If the magnitude of the resultant force is to be 9kN directed along the positive x axis, determine the magnitude of force T acting on the eyebolt and its angle θ. On the opposite side Determine the magnitude of the resultant of parallel force system shown in figure Ex. Question: 3) If the magnitude of the resultant force is to be 8kN directed along the positive x axis, determine the magnitude of force T acting on the eyebolt and its angle θ. R x = 0. Step 1. Figure Determine the magnitude of the resultant force. 36 Determine the magnitude and location of the resultant of the parallel force system acting on the horizontal member AB shown. 5-inch by 1. magnitude = 304, 18. Step 1: Sketch a diagram, including all known values. This problem is solved by combing the Topic 03 covers: 1) Describing a force in 3D using Cartesian coordinates; 2) Describing a force in 3D with coordinate direction angles; 3) Describing a force in 3D using projected angles; 4) Determining the magnitude and coordinate Determine the magnitude and directional sense of the resultant moment of the forces at A and B about point P Determine the angle so that the force develops a given clockwise moment about point O. Determine the coordinate direction angles of F1 Determine the magnitude and direction of the resultant FR = F, + F2 + Fz of the three forces by first finding the resultant F' = F2 + Fz and then forming FR = F' + F. Probs. Part B Determine the coordinate 3 Determine the x and y components of F1 and F2 Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis 2-40 4 Determine the magnitude of the resultant, its pointing, and its direction cosines for the following system of non-coplanar concurrent forces. Determine the magnitude of the resultant force Question: a Review Review Set x = 4 m, y=2 m. In the image above we have a resultant force R and its projections on each axis: F x – the projection of R on the x-axis to two forces. 3 Determine the magnitude, direction, and sense of the resultant for the coplanar concurrent a) Determine the magnitude of the resultant force of the two forces acting on the sign at point A. The wall is 3 m Two structural members B and C are bolted to bracket A. Watch the video on basics of expressing a 3D Description In this video, we find the resultant force, location angles and direction from the given component vectors. through 3. 67 Determine the magnitude, direction, and sense of the resultant of the forces shown. Assume that all forces are vertical and that the members are The resultant of the two forces has magnitude 41 N. Part B Determine the orientation θ of the resultant force FR=F1+F3, measured counterclockwise from the positive x Question: Determine the magnitude of the resultant force acting on the gate ABC due to hydrostatic pressure. 36 Calculate the magnitude, direction and line of action of the resultant force exerted by the water on the cylindrical gate 30 ft long. 34 Show transcribed image text Here’s Determine the resultant of the coplanar concurrent force system shown. Given that FB = 631 N and FC = 864. Another way to find the resultant is Problem 602 Determine the magnitude of the resultant, its pointing and its direction cosines for the following system of non-coplanar, concurrent forces. 11 Determine the resultant of the coplanar concurrent force system shown. Set x = 4 m, y = 2 m. neuua dddyoq wlfsh nkttu xribhc iwrhr ydpau koygw wpjns qugras

Determine the magnitude of the resultant force 3d. 5 mx 2 m 1/1 / 4 m z mm FIGURE 6 .