Answer to Question #317745 in Classical Mechanics for Johannes Steven

Question

The velocity, V, for the stream-line flow of a liquid in a small uniform tube depends on the radius, r, of the tube, the density, ρ, and the coefficient of viscosity, η, of the liquid. Use the method of dimensional analysis to obtain an expression for velocity. (5)

2. Show whether or not the following have similar dimensions:

(a) Young’s modulus and Stress (3) (b) Force and Power (3)

3. The position of a particle moving along the x-axis is given by x = 7t2 + 2t3, where x is in meters and t is in seconds. Determine the following, when t = 1.4 s:

(a) The position (2) (b) The velocity (2) (c) The acceleration (2)

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4. Letvectors 𝑨=𝑛𝑖̅−3𝑗̅+2𝑘 and𝑩 =3𝑖̅−2𝑗̅+3𝑘

(a) Find the scalar product of the two vectors. (3) (b) For n = 3, find the cross product of the two vectors. (4) (c) For n = 1, use the cross product to find the angle between the two vectors. (6)

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5. A vector 𝑹 has a direction of 30 with respect to the y-axis. Draw this vector and find

its x and y components if its magnitude is 7 m.

Answer 1

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