Determine whether the following equations are dimensionally homogeneous. 1 h 2 h represents a length, g is an acceleration, and t is a time.
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![Determine whether the following equations are dimensionally homogeneous.
1
16
2
h
h represents a length, g is an acceleration, and t is a time.
[h] = M^
LA
= M^
L^
T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc182e599-5dc6-4a45-9882-7fbf1677e7b9%2F51ca6968-999f-4630-8bbe-a88d22184b1b%2F6vnsxju_processed.png&w=3840&q=75)
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- . I am planning to perform some volume-flow rate measurements in the Fluid Mechanics Laboratory. For this, I need a volumetric measuring tank (graduated cylinder) and a stopwatch. I considered the volume of the measured tank as 15 gallons and a stopwatch with reaction time as 1/10th of a second (though resolution of 1/1000th of a second). What is the volume flow rate if it takes 5 minutes to fill a 15-gallon of tank? Determine the smallest division to be on the tank in order to estimate the volume flow rate within an accuracy of ± 0.05 gpm.m and n are orthogonal vectors. Let their component forms be defined as (mx, my) and (nx, ny) respectively, where all values are integers. mx+nx=-3 and nymy=40. If OWhen handwriting vectors, you must add arrows, etc. to indicate vector notation 1. You record the position of a moving object on a large planar surface as r = (2+1) i-² j (m), where t is in s. At t = 2 s, what is the magnitude of v and a, and what angle do they make with the +x direction? Include vector diagrams for both.The amount of time it takes for a pendulum to swing “to-and-fro” through one complete cycle is called the “period” and is calculated using the following equation: where T = period in seconds, I = mass moment of inertia, m = mass of pendulum in kilograms g = gravitational acceleration, 9.8 m/s2, h = effective length of pendulum in meters What is the appropriate unit for I if the preceding equation is to be homogeneous in units? Please show all of your work.physical quantities m, r, u, a, and t with dimensions [m] = M, [r]= L, [v] = LT, [a] = LT-2, and [t] = T. Enter the dimensional expression of the quantity on the right-hand side of each equation. Your answers may contain only M, L, T, and exponents. Assume that each of the following equations is dimensionally consistent. F = ma [F] =Check the following equation for dimensional homogeneity: mv = [₁² ( (Fcose) dt where m is mass, v is velocity, F is force, 0 is an angle, and t is time. Check that each term in the equation has the following dimensions: [MªLºTc] where you are to choose the coefficients a, b, c. Answers: a = i b= i C = ifx | 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. 5A silver dollar is dropped from the top of a building that is 1377 feet tall. Use the position function below for free-falling objects. s(t) = -16t + Vot + so (a) Determine the position and velocity functions for the coin. s(t) = v(t) = (b) Determine the average velocity on the interval [2, 3]. ft/s (c) Find the instantaneous velocities when t = 2 seconds and t = 3 seconds. v(2) = ft/s v(3) = ft/s (d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.) t = (e) Find the velocity of the coin at impact. (Round your answer to three decimal places.) ft/sThe 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?m Consider an object moving along a line with the given velocity v. Assume t is time measured in seconds and velocities have units of Complete parts a through c. S a. Determine when the motion is in the positive direction and when it is in the negative direction. b. Find the displacement over the given interval. c. Find the distance traveled over the given interval. v(t) = 3t² - 36t+105; [0,8] a. When is the motion in the positive direction? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. OA. For t-values that satisfy (Use a comma to separate answers as needed. Type your answers in interval notation.) B. The motion is never in the positive direction. b. Find the displacement over the given interval. c. Find the distance traveled over the given interval. v(t) = 3t² - 36t+105; [0,8]An engineer would like to create a formula to determine the force exerted by a river flow on a bridge column. The figure of the problem is shown here in front and top views. Front view 18 |h Water properties V, P, μ Top view of This problems is similar but not the same of the exercise I solved in the class notes. Note that there are more variables which may be relevant for this problem, such as the gravity g and the flow depth h. Use the Buckingham Pi Theory to find an expression for the force F. 1) What popular non-dimensional numbers do you see? 2) What is the expression of the force?Check the following equation for dimensional homogeneity: mu = (Fcos) at where m is mass, v is velocity, F is force, is an angle, and it is time. Check that each term in the equation has the following dimensions: [MOLT] where you are to choose the coefficients a, b, c. Answers: b= C= i iSEE MORE QUESTIONS