Question

In: Physics

Show that the equation v2=v02 −2g(y−y0) is dimensionally consistent. (use dimensional analysis)

Show that the equation v²=v₀² −2g(y−y₀) is dimensionally consistent. (use dimensional analysis)

Expert Solution

Given equation is:-

Where ,

: is the final velocity measured in .
: is the initial velocity measured in .
: is the acceleration due to gravity measured in
: is the position (or distance) measured in (meters).

Above physical quantities can be expressed in terms of some basic dimensions given below in SI units,

: Length in meters ()
: Time in seconds ()

Equation is,

The equation contains three terms as, V², V₀² and 2g (y - y₀) . In order to have consistency, all the three terms must have same dimensions.

Taking the equation in terms of dimensions as,

: Velocity =
: Velocity =
: Acceleration =
: distance =
: distance =

Therefore equation becomes,

As we can see, all the terms have unit of velocity square and have same dimensions. Thus the equation is dimensionally consistent.

genius_generous answered 5 months ago

y'' + 16y = (8)(cos(4t)) y0)= 0 y'(0)= 8 Use Laplace Transforms to solve. Sketch the...

y'' + 16y = (8)(cos(4t)) y0)= 0 y'(0)= 8 Use Laplace Transforms to solve. Sketch the solution or use matlab to show the graph.

Use Lagrange multipliers to show that the shortest distance from the point (x0,y0,z0) to the plane...

Use Lagrange multipliers to show that the shortest distance from the point (x0,y0,z0) to the plane ax+by+cz=d Is it the perpendicular distance? (Remind yourself of the equation of the line perpendicular to the plane.) How to solve it

Perform a dimensional analysis to obtain an equation for rising air bubble velocity, v. What variables...

Perform a dimensional analysis to obtain an equation for rising air bubble velocity, v. What variables would v depend on; i.e. what variables would you include in your analysis? Assume that v is a function of d (air bubble diameter). pw (density of water), g (gravitational acceleration), and uw (viscosity of water), and perform the dimensional analysis. How many dimensionless groups do you get (and why)? Look up the defintion of Reynolds number... Is Reynolds number of the dimensionless groups...

1) Use dimensional analysis to find a relationship between the force of the wind, F, on...

1) Use dimensional analysis to find a relationship between the force of the wind, F, on a car. You will also need the velocity, v, the surface area of the car, A and the density of air, p. . 2) Consider the problem of determining the terminal velocity of a raindrop falling from a motionless cloud. Determine a general model using dimensional analysis. Hint: You will need 5 parameters

Separate the wave equation in two-dimensional rectangular coordinates x, y. Consider a rectangular membrane, rigidly attache...

Separate the wave equation in two-dimensional rectangular coordinates x, y. Consider a rectangular membrane, rigidly attache to supports along its sides, such that a ≤ x ≤ 0 and b ≤ y ≤ 0. Find the solution, including the specification of the characteristic frequencies of the membrane oscillations. In the case of a = b, show that two or more modes of vibration correspond to a single frequency

Use dimensional analysis to determine the number of milliliters to administer a patient needing 4 mg...

Use dimensional analysis to determine the number of milliliters to administer a patient needing 4 mg of medication. The medication on hand is labeled 6 mg to 2 ml.

Use the dimensional analysis to find the D-dependance of the van der Waals interaction Energy between...

Use the dimensional analysis to find the D-dependance of the van der Waals interaction Energy between two semi-infinite bodies. N.B. : D is the distance between the two semi-infinite bodies.

Use the dataset and the predicted regression equation to calculate the expected value of Y for...

Use the dataset and the predicted regression equation to calculate the expected value of Y for each known value of X. Then, use this information to calculate the standard error of estimate. Round all values to the nearest whole number. Y’ = 2.5 + .75(ice cream sales) Ice Cream Sales Observed Crime Predicted Crime 10 5 20 20 30 30 20 25 30 15 10 10 Now, calculate the standard error. The standard error is _________ PLEASE show your work...

Show the effect of the following transactions of Avis Services on the accounting equation. Use “+”...

Show the effect of the following transactions of Avis Services on the accounting equation. Use “+” to denote an increase, “–” to denote a decrease and “0” to denote no change to the elements of the equation. Copy the table in your answer book and follow the example given. The business uses the periodic inventory system. ■ Assume that the bank balance is favourable at all times. Example: Paid the insurance premium by cheque, R500 ASSETS EQUITY LIABILITIES No. Equipment...

⦁ Use the equation of motion to show that once released from submersion the magnitude of...

⦁ Use the equation of motion to show that once released from submersion the magnitude of the acceleration a, for the object that ascends (floating to the surface), in terms of the density of the fluid and object is: a = (ρoil /ρo – 1)g ⦁ Use one of the previous equations to determine the density of the oil?