Physical quantities and measurement techniques：練習問題

Which of the following is a vector quantity?

A student uses a micrometer screw gauge to measure the diameter of a thin copper wire. The reading on the main scale is \(2.5\text{ mm}\) and the reading on the thimble scale is \(14\) divisions, where each thimble division represents \(0.01\text{ mm}\).

What is the diameter of the wire?

Two forces act on an object at right angles to each other. One force is \(6.0\text{ N}\) acting vertically upwards and the other is \(8.0\text{ N}\) acting horizontally to the right.

What is the magnitude of the resultant force?

Which of the following contains only scalar quantities?

A student uses a digital timer to measure the time taken for a pendulum to complete 20 full oscillations. The student records two separate readings: t₁ = \(32.4\text{ s}\) and t₂ = \(32.6\text{ s}\).

What is the average period of the pendulum?

State two precautions a student should take when using a ruler to measure the length of a laboratory bench to ensure the result is as accurate as possible.

A student determines the thickness of a single sheet of paper by measuring the total thickness of a stack of 500 sheets using a ruler. The total thickness is found to be \(4.5\text{ cm}\).

State the thickness of one sheet of paper in micrometres (\(\mu\text{m}\)).

An object is subjected to two forces. Force \(F_A\) has a magnitude of \(12.0\text{ N}\) acting due North. The resultant force acting on the object is \(15.0\text{ N}\) and acts in a direction of \(053.1^\circ\) (East of North).

By calculation or scale drawing, determine the magnitude of the second force, \(F_B\), acting due East.

A physicist is studying the motion of a small pendulum to determine an accurate value for its period of oscillation.

(a) The physicist uses a digital stopwatch to time 40 complete oscillations. The total time recorded is \(58.4\text{ s}\).
(i) Define the term period of a pendulum.
(ii) Calculate the period of this pendulum to an appropriate number of significant figures.

(b) Suggest one reason why timing 40 oscillations instead of 1 oscillation reduces the percentage uncertainty caused by the physicist's reaction time.

(c) If the physicist repeated the experiment and found the time for 40 oscillations to be \(58.6\text{ s}\) instead, calculate the new average period based on both sets of readings.

A physics student is investigating the dimensions and density of a specialized cylindrical copper alloy rod. The student uses a micrometer screw gauge to measure the diameter and a displacement method to find the volume.

(a) The student records the diameter of the rod at four different positions. The readings are: \(12.42\text{ mm}\), \(12.46\text{ mm}\), \(12.44\text{ mm}\), and \(12.44\text{ mm}\).
(i) Calculate the average diameter of the rod in mm.
(ii) The micrometer used has a zero error of \(+0.03\text{ mm}\). Determine the corrected average diameter of the rod.

(b) The student determines the volume of the rod by submerged displacement in a measuring cylinder containing water. The initial volume of water is \(60.0\text{ cm}^3\). When the rod is submerged, the new reading is \(82.5\text{ cm}^3\). Calculate the volume of the rod in \(\text{cm}^3\).

(c) The mass of the rod is found to be \(198.0\text{ g}\). Using the volume from part (b), calculate the density of the alloy in \(\text{g/cm}^3\).