Chapter 7, Problem 23RQ

6/85 In a study of head injury against the instrument panel of a car during sudden or crash stops where lap belts without shoulder straps or airbags are used, the segmented human model shown in the figure is analyzed. The hip joint O is assumed to remain fixed relative to the car, and the torso above the hip is treated as a rigid body of mass m freely pivoted at O. The center of mass of the torso is at G with the initial position of OG taken as vertical. The radius of gyration of the torso about O is ko. If the car is brought to a sudden stop with a constant deceleration a, determine the speed v relative to the car with which the model's head strikes the instrument panel. Substitute the values m = 50 kg, 7 = 450 mm, r = 800 mm, ko = 550 mm, 0 = 45°, and a = 10g and compute v. Answer v = 11.73 m/s PROBLEM 6/85

Using AutoCAD

340 lb 340 lb Δ

4. In a table of vector differential operators, look up the expressions for V x V in a cylindrical coordinate system. (a) Compute the vorticity for the flow in a round tube where the velocity profile is = vo [1-(³] V₂ = Vo (b) Compute the vorticity for an ideal vortex where the velocity is Ve= r where constant. 2πг (c) Compute the vorticity in the vortex flow given by Ve= r 2лг 1- exp ( r² 4vt (d) Sketch all the velocity and vorticity profiles.

In the figure, Neglects the heat loss and kinetic and potential energy changes, calculate the work produced by the turbine in kJ T = ??? Steam at P=3 MPa, T = 280°C Turbine Rigid tank V = 1000 m³ Turbine Rigid tank V = 100 m³ V = 1000 m³ V = 100 m³ The valve is opened. Initially: evacuated (empty) tank O a. 802.8 Initially: Closed valve O b. 572 O c. 159.93 Od. 415 e. 627.76 equilibrium

Please find the torsional yield strength, the yield strength, the spring index, and the mean diameter. Use: E = 28.6 Mpsi, G = 11.5 Mpsi, A = 140 kpsi·in, m = 0.190, and relative cost= 1.

A viscoelastic column is made of a material with a creep compliance of D(t)= 0.75+0.5log10t+0.18(log10t)^2 GPA^-1 for t in s. If a constant compressive stress of σ0 = –100 MPa is applied at t = 0, how long will it take (= t1/2) for the height of the column to decrease to ½ its original value? Note: You will obtain multiple answers for this problem! One makes sense physically and one does not.

A group of 23 power transistors, dissipating 2 W each, are to be cooled by attaching them to a black-anodized square aluminum plate and mounting the plate on the wall of a room at 30°C. The emissivity of the transistor and the plate surfaces is 0.9. Assuming the heat transfer from the back side of the plate to be negligible and the temperature of the surrounding surfaces to be the same as the air temperature of the room, determine the length of the square plate if the average surface temperature of the plate is not to exceed 50°C. Start the iteration process with an initial guess of the size of the plate as 43 cm.   The properties of air at 1 atm and the film temperature of (Ts + T)/2 = (50 + 30)/2 = 40°C are k = 0.02662 W/m·°C, ν = 1.702 × 10–5 m2 /s, Pr = 0.7255, and β = 0.003195 K–1.         Multiple Choice   0.473 m   0.284 m   0.513 m   0.671 m

A 40-cm-diameter, 127-cm-high cylindrical hot water tank is located in the bathroom of a house maintained at 20°C. The surface temperature of the tank is measured to be 44°C and its emissivity is 0.4. Taking the surrounding surface temperature to be also 20°C, determine the rate of heat loss from all surfaces of the tank by natural convection and radiation. The properties of air at 32°C are k=0.02603 W/m-K, v=1.627 x 10-5 m²/s, Pr = 0.7276, and ẞ = 0.003279 K-1 The rate of heat loss from all surfaces of the tank by natural convection is The rate of heat loss from all surfaces of the tank by radiation is W. W.