5. A candy company distributes boxes of chocolates with a mixture of creams, toffees, and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees, and cordials vary from box to box. For a randomly selected box, let X and Y represent the weights of the creams and the toffees, respectively, and suppose that the joint density function of these variables is - (24xy, 0s x< 1, 0
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- 1. N is inversely proportional to the square of x and when x = 2, N = 50. What is N when x = 5?Cross-section of an object (having same section normal to the paper) submerged into a fluid consists of a square of sides 2 m and triangle as shown in the figure. The object is hinged at point P that is 1 m below the fluid free surface. If the object is to be kept in the position as shown in the figure, the value of x should be 2m 2m- RY X 4 4 += 1mThe cantilevered beam shown in the accompanying figure is used to support a load acting on a balcony. The deflection of the centerline of the beam is given by the following equation: y = deflection at a given x location (m)w = distributed load (N/m)E = modulus of elasticity (N⁄m2 )I = second moment of area (m4 )x = distance from the support as shown ( x )L = length of the beam (m) Using Excel, plot the deflection of a beam whose length is 5 m with themodulus of elasticity of E = 200 GPa and I = 99.1×106 mm4 . The beam is designed to carry a load of 10,000 N/m. What is the maximum deflection of the beam?
- 5.) The figure shows a metal hanging by a thin wire from a floating wood block. The wood block has a specific gravity Sb =0.25, a square base of 80 mm x 80 mm and height of 15 mm. The metal has a volume of 8000 mm^3. Using a unit weight of water 9800 N/m^3 and g=9.80 m/s^2., find the mass of metal in grams. Write your answer in two decimal places. fluid mechanicsA person by the name of Huebscher developed a relationship between theequivalent size of round ducts and rectangular ducts according to D = diameter of equivalent circular duct (mm)a = dimension of one side of the rectangular duct (mm)b = the other dimension of the rectangular duct (mm)Using Excel, create a table that shows the relationship between the circular and the rectangular duct dimensions, similar to the one shown in the accompanying table.QUESTION 3 A plank L m long is placed in a horizontal position with its ends resting on two inclined planes as shown. The angle of friction is p. Determine how close the load P can be placed near B before slipping impends. A x = L 81 82 02 8 35 40 20 Answer in three (3) decimal places: L m m deq deg deg 01 B
- Consider the beam shown in (Figure 1). Suppose that a = 150 mm , b = 250 mm , c = 50 mm . Part A Determine the moment of inertia of the beam's cross-sectional area about the centroidal x axe. Express your answer to three significant figures and include the appropriate units. HA ? I = Value Units Submit Request Answer Part B Determine the moment of inertia of the beam's cross-sectional area about the centroidal y axe. Express your answer to three significant figures and include the appropriate units. HA ? Iy = Value Units Submit Request Answer Figure 1 of 1 Provide Feedback a aA mechanism shown in the figure consists of equally long steel and copper wires which carry the applied load in equal shares. What shall be the ratio of the diameter of the copper wire to that of the steel wire, when both the wires undergo equal strains ? Steel wire Es = 200 GPa (a) √2 (c) √/12/2 Copper wire Ec = 100 GPa (b) 1.0 (d) 1|2the value of D=9 , C=2.5 , AND B=25
- 6.21 A cantilever beam shown in the accompanying figure is used to support a load acting on a balcony. The deflection of the centerline of the beam is given by the equation: - wx? y= -(x² – 4 Lx + 6L²) 24 EI where y = deflection at a given x location, (m) w = distributed load E = modulus of elasticity (N/m²) I = second moment of area (m²) x = distance from the support as shown (m) L = length of the beam (m) What is the appropriate unit for w if the preceding equation is to be homogeneous in units? Show all steps of your work. Problem 6.21 A cantilever beam.As we explained in Chapter 10, viscosity is a measure of how easily a fluid flows. For example, honey has a higher value of viscosity than does water because if you were to pour water and honey side by side on an inclined surface, the water will flow faster. The viscosity of a fluid plays a significant role in the analysis of many fluid dynamics problems. The viscosity ofwater can be determined from the following correlation:μ = c1 10c2 1(T−c3 )whereμ = viscosity (N/s.m2 )T = temperature (K)c1=2.414×10-5 (N/s.m2 ) c2= 247.8 K c3= 140 KUsing Excel, create a table that shows the viscosity of water as a function oftemperature in the range of 0° C (273 15 ) to 100° C (373 15 ) in increments of 5° C. Also create a graph showing the value of viscosity as a function of temperature.The air resistance to the motion of a vehicle is something important that engineers investigate. As you may also know, the drag force acting on a car is determined experimentally by placing the car in a wind tunnel. For a given car, the experimental data is generally represented by a single coefficient that is called the drag coefficient. It is given by the relationship: Fa C, = where C, = drag coefficient F, = measured drag force (Ib) p = air density (slugs/ft') V = air speed inside the wind tunnel (ft/s) A = frontal area of the car (ft²) What is the appropriate unit for C, if the preceding equation is to be homogeneous in units? Show all steps of your work.