In the dimensionally homogenous equation :
Tau = (P/A) +((T)(r))/J
Tau is a stress (force per unit area), A is an area, T is a torque (force times distance) and r is a length. Determine the dimensions of P and J.
In the dimensionally homogenous equation : Tau = (P/A) +((T)(r))/J Tau is a stress (force per...
Prove the fractional change in the acceleration due to gravity at a distance 6r above the earth's surface is given by -2dr/r, where r is the mean radius of the earth. At what is distance above the earth's surface has the acceleration due to gravity decreased by 2% compared to the mean value of 9.81 m/s^2 observed at the earth's surface? In the dimensionally homogeneous equation sigma = 3P/A -Tr/pi Q, find the dimensions of P and Q if sigma...
1. Conceptual questions a. Is the following equation dimensionally homogeneous? Here, T is torque and wis angular velocity. Explain your answer. P2 1 P1 - + - d P 2 Τω gz, + - 21 = - + - 0 p 2 ' m b. The following is Euler's equation for turbine power. Where Pturbine is the power output of the turbine, p is the density of water, and Vti is the tangent velocity of the turbine blades at the...
2) A. Linearize the following equation where s and t are the variables: pep B. What are the slope and intercept of your new equation? C. Check that your new equation is dimensionally correct (s is a distance, v is a velocity, a is an acceleration, and t is a time) 3) A. Linearize the following equation where D and h are the variables: B. What are the slope and intercept of your new equation? C. Check that your new...
Tensile strain is: A) the stress per unit area B) the same as force C) the ratio of stress to elastic modulus D) the applied force per cross-sectional area E) the ratio of the change in length to the original length
Materials fracture when the force per unit area, called STRESS, exceeds a critical value. In general, the critical stress depends on the direction as well as the magnitude of the force. For example, bones break differently when subjected to torsional (twisting) stress than when subjected to compressional (or squeezing) stress. Let us consider compressional stress. Wet human bone for 20-39 year olds has an ultimate compressive strength of 1.6x104N/cm2 [8]. Consider a person who falls from a height to the...
problem 40 with parts 40. The atmospheric pressure (force per unit area) on a surface at an altitude z is due to the weight of the column of air situated above the surface. Therefore, the difference in air pressure p between the top and bottom of a cylindrical volume element of height Az and cross-section area A equals the weight of the air enclosed (density ρ times volume V-: ΑΔε times gravity g), per unit area: Let Δ、→0 to derive...
[4 marks) (Scaling) In Fisher's equation, и Ut = DUcx + ru(1 K the variables t, 2, and u have dimensions is time, length, and population (animal) per area respectively. The parameters are the growth rate r with units of 1/time, the carrying capacity K with units of population (animals) per area and the diffusion constant D with dimensions length-squared per time. Use the following scales to build dimensionless variables and rewrite the equation in a dimensionless form. t х...
A circular bar of radius r under axial force P and torque T will elongate by an amount e and twist through and angle θ. Find Poisson’s ratio for an isotropic material (inc. steps)? 1. A circular bar of radius r under axial force P and torque T will elongate by an amount e and twist through and angle 0. Show that Poisson's ratio for an isotropic material is given by Pr? 4Te (This answer suggests a convenient experimental method...
2. Using Maxwell's stress tensor, calculate the force per unit length of electric attraction between the two parallel wires that each carry a linear charge density separated by a distance 2a. (Hint. Integrate along a plane equidistant between the wires.]
i got 1.4 but it was incorrect and i am not sure why. Please help! READING 2 Materials fracture when the force per unit area, called STRESS, exceeds a critical value. In general, the critical stress depends on the direction as well as the magnitude of the force. For example, bones break differently when subjected to torsional (twisting) stress than when subjected to compressional (or squeezing) stress. Let us consider compressional stress. Wet human bone for 20-39 year olds has...