Part A Cables of negligibie weight support the loading shown. (Figure 1) if W - 85.0 N. W, - 510 N. ya- 1.40 m. yc - 2.80 m yD -0.700 m. and ze - 0.850 m. find zB Express your answer numerically in meters to three significant figures. > View Available Hint(s)
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- Learning Goal: To calculate minor head losses and pressure drops for pipe fittings. Minor losses in pipe flow are the result of disruptions to the steady laminar or turblent flow in a pipe by entrances, bends, transitions, valves or other fittings. In general, calculating these losses analytically is too complex. However, all of these losses can be modeled using terms of the form h = KL where Kr, is called the loss coefficient and is determined experimentally. This coefficient relates the minor head loss to the velocity head for the flow. For expansions and contractions, the loss coefficient is calculated using nine the velocity for the smaller diameter pipe. The table below gives some representative values for various minor head losses. These are representative only, and a more complete table would account for different kinds of fittings and connections (like threaded or soldered). Fitting Well-rounded entrance ≥0.15 Flush entrance Re-entrant pipe Discharge pipe Sudden contraction (d₂…Learning Goal: To determine the effects of certain geometric shapes, namely fillets and circular cutouts, on the stress distributions inside a rigid body and to determine the maximum applicable axial force in the same rigid body while considering these stress concentrations. The member shown below is made of steel (oallow = 145 MPa ) that is 80 mm thick. The member is subjected to an axial force P that is applied at both ends. Let rf = 10 mm , w = 120 mm , h = 40 mm , and d = 25 mmLearning Goal: To understand the concept of moment of a force and how to calculate it using a scalar formulation. The magnitude of the moment of a force with a magnitude F around a point O is defined as follows:Mo = Fdwhere d is the force's moment arm. The moment arm is the perpendicular distance from the axis at point O to the force's line of action. Figure F₁ 1 of 2 Part A A stool at a restaurant is anchored to the floor. When a customer is in the process of sitting down, a horizontal force with magnitude F₁ is exerted at the top of the stool support as shown in the figure. (Figure 1) When the customer is seated, a vertical force with magnitude F2 is exerted on the stool support. If the maximum moment magnitude that the stool support can sustain about point A is M₁ = 140 lb-ft, what is the maximum height do that the stool can have if the magnitudes of the two forces are F₁ = 65.0 lb and F₂ = 140 lb ? Assume that moments acting counterclockwise about point A are positive whereas…
- Learning Goal: To use fundamental geometric and statics methods to determine the state of plane stress at the point on an element of material that is rotated clockwise through an angle from the in- plane stress representation of the point. The state of in-plane stress at a point on an element of material is shown. Let o, the same point that is rotated through an angle of 0-35 45.0 ksi, o, 19.0 ksi, and Ty 12.0 kai. Use this information to represent the state of stress ofPhysics 121 Spring 2021 - Document #11: Homework #04 & Reading Assignment page 4 of 8 Problem 1: Gnome Ride - This from a Previous Exam I. A Gnome of given mass M goes on the Gnome Ride as follows: He stands on a horizontal platform that is connected to a large piston so that the platform is driven vertically with a position as a function of time according to the following equation: y(t) = C cos(wt) Here w is a constant given angular frequency, C is a given constant (with appropriate physical units) and y represents the vertical position, positive upward as indicated. Part (a) - What is the velocity of the Gnome at time t = 0? Explain your work. Present your answer in terms of the given parameters Part (b) – What is the net force on the Gnome at time t = 0? Explain your work. Present your answer in terms of the given parameters Part (c) – What is the Normal Force on the Gnome at time t = 0? Explain your work. Present your answer in terms of the given parameters Some Possibly Useful…Learning Goal: To use the principle of linear impulse and momentum to relate a force on an object to the resulting velocity of the object at different times. The equation of motion for a particle of mass m can be written as EF dv = ma = m dt By rearranging the terms and integrating, this equation becomes the principle of linear impulse and momentum: t2 ES F dt = m f dv = mv2 – mv1 V1 For problem-solving purposes, this principle is often rewritten as mvị +£ F dt = mv2 The integral F dt is called the linear impulse, I, and the vector my is called the particle's linear momentum. A tennis racket hits a tennis ball with a force of F = at – bt?, where a = 1200 N/ms , b = 500 N/ms? , and t is the time (in milliseconds). The ball is in contact with the racket for 3.05 ms . If the tennis ball has a mass of 62.6 g, what is the resulting velocity of the ball, v, after the ball is hit by the racket? Express your answer numerically in meters per second to three significant figures. • View Available…
- Learning Goal: Use the two loadings below and the principle of superposition to answer the following questions. To use the method of superposition to calculate a beam deflection and slope. For beams with small deflections, the assumptions for using the method of superposition apply: the deflections and slopes are linearly related to the load, and the deflections do not significantly change the original geometry of the beam. Load The deflections and slopes for beams subjected to multiple loads can then be found using linear combinations known results for individual loads. -(--4) -5w L 384EI -5wz Lª 768EI -w L -3wz L" 24EI 128EI w L 24EI 7wz L" 384EI OR Part A - Determine the load combination A beam is subjected to the loading shown (Figure 1) where wa = 2 kN/m and w, = 2.5 kN/m. Describe the loading as a linear combination of the loads in the above table. Express your answers in kN/m. • View Available Hint(s) VOAEO If vec ? Figure w1, w2= |2.4, –.7 kN/m Submit Previous Answers X…You have been contracted by a company to design a system for them. The system requires that you use a very elastic material but the materials available to you are Material A which has a Young’s Modulus of 210,000 N/mm2 and Material B which has a Young’s modulus of 12,500 N/mm2 Using the deflection and stiffness equation, which material will best suit the job?Learning Goal: To understand the derivation of the law relating height and pressure in a container. In this problem, you will derive the law relating pressure to height in a container by analyzing a particular system. A container of uniform cross-sectional area is filled with liquid of uniform density . Consider a thin horizontal layer of liquid (thickness ) at a height as measured from the bottom of the container. Let the pressure exerted upward on the bottom of the layer be and the pressure exerted downward on the top be . Assume throughout the problem that the system is in equilibrium (the container has not been recently shaken or moved, etc.). What is Fup , the magnitude of the force exerted upward on the bottom of the liquid?
- Learning Goal: To be able to add and subtract vectors using geometric and vector addition. A brother and sister are playing in the woods, when suddenly the brother realizes that they are separated. The last place he remembers seeing his sister is at a particularly large tree. The brother traveled d₁ = 21.0 m at 0₁ = 26.0° from the tree then turned and traveled 4 = d2 11.0 m at 02 = 140°. Meanwhile, the sister traveled d3 = 17.5 m at an angle of 03-117° from the tree. The angles are given with respect to east with counterclockwise being defined as positive(Figure 1) Figure d3 03 d₂ 0₁ 0₂ d₁ 1 of 4 X > v Confect Part C Distance to home - After the boy has found his sister, they want to travel the shortest path home. If their home is located = d4 75 m due north of the big tree, what is the magnitude and direction of the displacement from the siblings to their home, dBGH?(Figure 4) Express your answers, separated by a comma, to three significant figures. Enter the angle measured…The director of the swimming club runs an experiment by examining the impact of 11 factors on average race times across 6 swimming tournaments (6 experimental runs). (Choose all that are true) The full model should be fit as the higher order interactions are likely to matter and there are sufficient degrees of freedom for it. The design is a supersaturated design because the number of factors is greater than the number of runs - 1. Backwards selection should be used to determine which factors significantly impact race times as model refinement will be needed. Forwards selection should be used to determine which factors significantly impact race times as model refinement will be needed and there are insufficient degrees of freedom to fit the full model.Learning Goal: To calculate the normal and shear stresses at a point on the cross section of a column. A column with a wide-flange section has a flange width b = 250 mm , height k = 250 mm , web thickness to = 9 mm , and flange thickness t; = 14 mm (Figure 1). Calculate the stresses at a point 65 mm above the neutral axis if the section supports a tensile normal force N = 2 kN at the centroid, shear force V = 5.8 kN , and bending moment M = 3 kN - m as shown (Figure 2). The state of stress at a point is a description of the normal and shear stresses at that point. The normal stresses are generally due to both internal normal force and internal bending moment. The net result can be obtained using the principle of superposition as long as the deflections remain small and the response is elastic. Part A- Normal stress Calculate the normal stress at the point due to the internal normal force on the section. Express your answer with appropriate units to three significant figures. • View…