Physical quantities and units：練習題

Which of the following is equivalent to a length of \(150 \, \text{nm}\)?

Thermal energy capacity is defined as the energy required to raise the temperature of an object by one kelvin. What are the SI base units of thermal energy capacity?

The resistive force \(F\) acting on an object moving through a fluid at speed \(v\) can be modeled by the equation \(F = Av + Bv^2\), where \(A\) and \(B\) are constants. What are the SI base units of the constant \(B\)?

How many nanoseconds (ns) are equivalent to one megasecond (Ms)?

Which of the following represents the SI base units for the electrical resistance of a component?

State the SI base unit for thermodynamic temperature and recall the meaning of the prefix 'pico'.

The drag force \(F\) on a sphere of radius \(r\) moving at velocity \(v\) through a fluid is given by the equation \(F = 6\pi \eta r v\). Determine the SI base units of the coefficient of viscosity \(\eta\) by checking the homogeneity of the equation.

Two coplanar forces, one of \(6.0 \, N\) acting due North and another of \(8.0 \, N\) acting due East, are applied to a point mass. Calculate the magnitude and the bearing of the resultant force.

The equation relating pressure \(P\), density \(\rho\), acceleration of free fall \(g\), and height \(h\) is given as \(P = \rho gh\).

(a) State the SI base units for each of the quantities \(P\), \(\rho\), \(g\), and \(h\).

(b) Show that the equation \(P = \rho gh\) is homogeneous with respect to units.

The rate of heat flow \(P\) through a solid material of thermal conductivity \(k\) is given by the equation \(P = kA\frac{\Delta T}{L}\), where \(A\) is the cross-sectional area, \(\Delta T\) is the temperature difference across the material, and \(L\) is the thickness of the material.
(a) Determine the SI base units of thermal conductivity \(k\).
(b) A specific insulation material has a thermal conductivity of \(24 \text{ mW m}^{-1} \text{ K}^{-1}\). Express this value in SI base units using scientific notation.