Problem 1 Dimensional Analysis Express the units of the following quantities in

Question

Problem 1 Dimensional Analysis Express the units of the following quantities in terms of the SI base units (m, kg, s). Show all relevant equations that you use to determine the dimensions of these quantities (eg. 1-mr for a point mass). a) Force, F b) Energy, E c) Spring constant, k d) Moment of Inertia, I Problem 2 Basic Data Analysis Calculate the mean and standard deviation of the following velocity measurements v (m/s) 25 32 30 Measurement Problem 3-Atwood Machine a) Using Newton's 2nd Law, derive the acceleration of the two-mass system shown below b) Letting mh = 3 kg and m2 = 5 kg, compute the acceleration of the two masses c Which direction does the system accelerate? (clockwise or counter-clockwise) m2 mi

Explanation / Answer

(a) Force is measured as F = ma, where is "a" is acceleration, which is defined as rate of change of velocity (V/t). Velocity is rate of change of displacement (d/t)

therefore, F = m x (V / t) = m x (d / t^2)

Since mass (m) is in Kg, Displacement (d) is in metre (m), and time is Seconds (s).

Therefore the units for Force is = Kg.m / s^2

(b) Energy is defined as the capacity to do work. i.e. Energy will have the units of workdone.

Work done is measured as w = F.S, where is F is force and S is dispacement

Since, as previously explained., F has units "Kg.m/s^2" and displacement has units of metre (m)

Units for Energy E = W = Kg.m^2 / s^2

(c) Sprink Constanst (k) comes in the spring force equation. i.e. F = -Kx, where x = displacement.

The units of Spring constant , k= F/x = Kg.m/s^2 .m = Kg/s^2

(d) Moment of Inertia (I) is measured with equation I = mr^2

therefore Units = Kg.m^2

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