Determine whether the following equations are dimensionally homogeneous. pl t = mf I represents an acceleration, p is a pressure, m is a mass, t is a time, and f is a force. [t] F pl = F^ LA mf
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- A cart weighing 0.5 kg is drawn up a smooth 45° incline by a motor, M, winding up a cable. The force in the cable can be expressed as 5t² N, where t is in seconds. When t = 0, the displacement s = 0 and the initial velocity is 3 m/s. Find the cart's velocity when t = 2 seconds. > Draw a very clear FBD of the cart that you can use to write the equations of motion > Write the equations governing the cart's motion along the incline. Use axes parallel and perpendicular to the incline. Find the velocity requestedGiven: The plane accelerates in its current trajectory with a= 100 m/s^2 Farag Angle theta= 5° W=105 kips F_drag= 80 kips m= 1000 lbs Find: F_thrust, F_lift Please include the KD. Fthrust Futel t Fueight 000 BY NC SA 2013 Michael SwanbomThe 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: Cd = Fd/(1/2)pV2A. What is the appropriate unit for Cd if the preceding equation is to be homogeneous in units?
- Water X 50-mm inside diameter The volume flow rate of the system The pressure at the point "A" The pressure at the point "B" 25-mm diameter As a consultant at one of the country's leading soft drink companies, you are tasked with evaluating the system depicted to determine the following parameters using Bernoulli's Equation if the values assigned to "X" and "Y" are 3m and 0.5m respectively: i. ii. iii.1.75m 1.5 m 2.75m Given: G/0 Find: 2.25m 6 o B 2.0m . h = 2.05 meters • Tension = 85 Newtons 26 1.5m W Magnitude of internal axial force (Newtons) Axial Force Bending moment V Shear forceThe dependence of thermal conductivity of a material on temperature is given by an empirical equation k = a ebT where a and b are constants, and k is in W/m-K and T is in K. Spot the true statement from the following set. a, a and b have the same dimension as k. b. a has the dimension of k and b is dimensionless. c. a and b are dimensionless. d. a has the dimension of k and b has the dimension of T.
- The left side of this equation tells how much energy Q the cylinder gives to the water while it cools. The right side of this equation tells how much energy Q the water and aluminum cup absorb from the cylinder to warm up. Because it is the same energy, they are equal. What is known in this equation? Mcyl 411.7 g, malum 46.5 g, malum+water = 175 g Can you find: mwater =? g Twater = Talum = 20°C (water and cup of room temperature) 90°C, T; = 35°C (hot cylinder and cool "cylinder+cup+water" temperatures) Tcyl kCal Calum = 0.22, Cwater 1 (specific heat of water and aluminum, measured in units kg-°C What are we looking for is Ccul - How we find it? Plug all the numbers into the equation (1), Ccul will be one unknown which you can calculate from the equation. Important, convert all the masses from grams to kilograms! After you find Ccyl, compare it to known value for the copper 0.093(our cylinder is made out of copper). |Ceyl -0.093| % : · 100% 0.093fx | А В 1 Variable Value Units Length 30 inch Width 18 inch 4 Area m^2 4 The image above shows a section of a Google sheet. What formula should be written in cell B4 to calculate the area in m^2 of a rectangle with a length value in B2 and width in B3? a) =length * width / (2.54)^2 b) =(B2*2.54e-2) * (B3*2.54e-2) с) %3[В2/2.54e-2) * (В3/2.54e-2) d) =(B2/2.54) * (B3/2.54) e) =length * width f) =(B2*2.54) * (B3*2.54) Page 2. 51:19 P N{ l 100% I A docs.google.com A block of mass m = 2 kg is attached to a spring with spring constant k = 200 N/m, and is set to oscillate on a friction-less horizontal surface. At time t = 0 its position is xO = 0 and its velocity is vo = +5 m/s. If the displacement is a cosine function, x(t)=A cos(wt+p), then which answer is correct about the oscillation amplitude A and the phase constant,p,: A = 0.25 m, and p = - T/2 A = 0.5 m, p = 0 A = 0.5 m, and p = r/2 A = 0.5 m, p = -T/2 A = 0.25 m, and p = t/2 Other: A body oscillates with simple harmonic frictionless motion along the x-axis. Its displacement varies ith time according to x(t)=0.5 cos(Tt). The ues of the velocity (in m/s) and acceleration (in m/s^2) of the 8 II
- A simple model of blood flow through the descending aorta is provided at the right. Total flow into the aorta is given by Q. The model includes the effects of vessel taper and outflow through 10 tributary arteries, through which the flow is assumed to be equal and given by q. We will assume that the blood is in-viscid and that the flow is steady and laminar. The effects of gravity are neglected. A₁ P₁ A₂ P₂ Find the pressure (P2) at bottom outlet in terms of Q, P₁, and A₁ for the three cases: a) For a tapered vessel for which A2 = A₁/2; and q = 0. b) For a vessel without a taper, but with q = Q/20. c) For a tapered vessel for which A2 = A₁/2 and q = Q/20.The kinetic energy and potential energy are the forms of energy microscopic mscroscopic variable staticThe modulus k of a coil spring (force required to stretch the spring a unit distance) can be expressed in equation form as k=(Gr^4)/(4R^3n) in which r and R are lengths and n is a dimensionless number. Determine the dimensions of G (a property of the spring material) .