The piston displacement $d$ can be written as $d = -4.0\cos(220t)$, with $d$ in centimetres.
State the separation between the lowest position AB and the highest position CD of the top surface of the piston.
Find the number of oscillations the piston makes each second.
On Fig. 3.1, draw a line to show the top surface of the piston when the piston’s speed is at its maximum.
Calculate the maximum speed of the piston.
The engine of a car contains several cylinders. Fig. 3.2 shows three of them. X is the same cylinder and piston as in Fig. 3.1. Y and Z are two additional cylinders, and the lowest and highest positions of the top surface of each piston are shown. Each piston oscillates with the same frequency, but the pistons are not in phase. At a given instant, the top of the piston in cylinder X is in the position shown.
In cylinder Y, the piston’s oscillations lead those of the piston in cylinder X by a phase angle of $120^{\circ}$ ($\frac{2\pi}{3}\,\text{rad}$). For this instant, complete the diagram of cylinder Y by drawing a line to show the top surface of the piston.
In cylinder Y, show the piston’s direction of movement by adding an arrow.
In cylinder Y, the piston’s oscillations lead those of the piston in cylinder X by a phase angle of $120^{\circ}$ $(\frac{2\pi}{3}\ \text{rad})$. For this instant, complete the diagram of cylinder Y by drawing (1) a line to show the top surface of the piston, and (2) an arrow to show the direction of movement of the piston.
In cylinder Z, the piston’s oscillations lead those of the piston in cylinder X by a phase angle of $240^{\circ}$ $(\frac{4\pi}{3}\ \text{rad})$. For this instant, complete the diagram of cylinder Z by drawing (1) a line to show the top surface of the piston, and (2) an arrow to show the direction of movement of the piston.
Calculate the speed of the piston in cylinder Y for this instant.