Question
A sphere of radius 2.1mm falls with terminal (constant) velocity through a liquid, as shown in Fig. 1.1.
Fig. 1.1
Three forces act on the moving sphere. The weight of the sphere is \(7.2\times 10^{-4}N\) and the upthrust acting on it is \(4.8\times 10^{-4}N\). The viscous force \(F_{V}\) acting on the sphere is given by
\(F_{V} = krv\)
where \(r\) is the radius of the sphere, \(v\) is its velocity and \(k\) is a constant. The value of \(k\) in SI units is \(17\).
(a) Determine the SI base units of \(k\).
(b) Use the value of the upthrust acting on the sphere to calculate the density \(ρ\) of the liquid.
(c) (i) On the sphere in Fig. 1.1, draw three arrows to show the directions of the weight W, the upthrust U and the viscous force \(F_{V}\). Label these arrows W, U and \(F_{V}\) respectively.
(ii) Determine the magnitude of the terminal (constant) velocity of the sphere.
Answer/Explanation
Ans:
Question
(a) Use an expression for work done, in terms of force, to show that the SI base units of energy are kg\(m^2 s^{–2}\).
(b) (i) The energy E stored in an electrical component is given by
\(E=\frac{Q^2}{2C}\)
where Q is charge and C is a constant.
Use this equation and the information in (a) to determine the SI base units of C.
SI base units …………………………………………………
(ii) Measurements of a constant current in a wire are taken using an analogue ammeter.
For these measurements, describe one possible cause of:
1. a random error
2. a systematic error.
Answer/Explanation
Answer:
(a) (work =) force × displacement
units: \(kg m s^{–2} × m = kg m^2 s^{–2}\)
(b) (i) units of Q: As
units of \(C: kg^{–1} m^{–2} A^2 s^4\)
(ii) 1. e.g. reading scale from different angles
(wrongly) interpolating between scale readings/divisions
2. e.g. zero error
wrongly calibrated scale