[OCR Extract] 8

Topic: Mechanics

Read the passage below and answer the questions that follow. Despite the increasing popularity of laser printers, inkjet printers remain a common choice for many people who are looking to print documents and photos from their computers due to their relatively low cost, smaller size and ability to print photos with better quality than laser printers. In inkjet printers, tiny droplets of ink are ejected and directly applied onto the paper, which then form the text or image. Traditionally, there are two main technologies used for droplet ejection in inkjet printers: continuous inkjet (CIJ) and drop-on-demand (DOD). In CIJ printers, a vibrating nozzle ejects a stream of regularly spaced ink droplets at a high velocity towards a pair of charging electrodes that deposits electrons on the droplets, giving the appropriate amount of charge to each droplet. The charged droplets then enter a region of uniform electric field between two deflection plates, which causes the droplets to deflect by different amounts corresponding to the amount of charge deposited on them. These droplets finally land on the piece of paper to form the desired image. This process in a CIJ printer is shown in Fig. 8.1. Fig. 8.1 Not every ink droplet that passes through the charging electrodes will get charged - instead, charged droplets will usually be separated by one or more uncharged "guard droplets". These uncharged droplets, which will not be deflected by the electric field, will enter a gutter that will divert these unused droplets back into the ink reservoir to be reused. Typical data for a commercial CIJ printer are given in Table 8.1. Table 8.1 | velocity of ink droplets $/ \mathrm{m} \mathrm{~s}^{-1}$ | 20 | | :-- | :-- | | frequency of droplet ejection $/ \mathrm{kHz}$ | 110 | | average diameter of ink droplet $/ \mu \mathrm{m}$ | 80 | | density of ink $/ \mathrm{g} \mathrm{cm}^{-3}$ | 0.84 | | p.d. across deflection plates $/ \mathrm{V}$ | 10000 | In DOD inkjet printers, ink droplets are ejected from a nozzle one drop at a time. While there are a number of different methods by which the droplets are ejected out individually, a common method used is called the thermal inkjet, or sometimes known as the "bubble jet". In thermal inkjet printers, the printhead consists of an ink chamber connected to a nozzle from which the ink will be ejected. There is a square-shaped thin-film resistor of sides length $20 \mu \mathrm{m}$ that acts as a heating element on top of the ink chamber. A small pulse of current is passed through the thin-film resistor, which quickly heats up and vapourises a thin layer of ink just below the thin-film resistor. This creates a bubble which expands rapidly. The pressure within the ink chamber increases and pushes a tiny drop of ink out of the nozzle onto the paper underneath to form the desired image. This process in a thermal inkjet printer is shown in Fig. 8.2. Fig. 8.2 Typical data for a commercial thermal inkjet printer are given in Table 8.2. Table 8.2 | velocity of ink droplets $/ \mathrm{m} \mathrm{~s}^{-1}$ | 4.5 | | :-- | :-- | | frequency of droplet ejection $/ \mathrm{kHz}$ | 18 | | average diameter of ink droplet $/ \mu \mathrm{m}$ | 10 | | density of ink $/ \mathrm{g} \mathrm{cm}^{-3}$ | 1.17 | | specific heat capacity of ink $/ \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1}$ | 2090 | | specific latent heat of vaporisation of ink $/ \mathrm{kJ} \mathrm{kg}^{-1}$ | 444 | | boiling point of ink $/{ }^{\circ} \mathrm{C}$ | 80 | | resistance of thin-film resistor $/ \Omega$ | 30 | [28.0m]

Part 1: (a) Fig. 8.3 shows a close-up of a series of spherical ink droplets travelling between the charging electrodes in a CIJ printer. Droplets A and B are two adjacent droplets. Fig. 8.3 Assume that the velocity of the droplets remains constant over its time of flight through the charging electrodes. (i) Using the data given, determine 1. the distance $d$ between droplets $A$ and $B$, $$ d=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $$ [2m]

Part 2: 2. the mass of each droplet. $$ \text { mass }=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \text { kg } $$ [2m]

Part 3: (ii) If droplets $A$ and $B$ are each charged uniformly with $-1.0 \times 10^{-13} \mathrm{C}$, 1. show that the electrostatic force between the droplets is 2.7 nN , [1m]

Part 4: 2. calculate the acceleration experienced by either droplet due to the electrostatic force in (a)(ii)1. acceleration =$ \qquad$ $\mathrm{m} \mathrm{~s}^{-2}$ [1m]

Part 5: (iii) Suggest why "guard droplets" are necessary between two charged particles in the stream of ink droplets in a CIJ printer. [2m]

Part 6: (b) Fig. 8.4 shows the deflection plates of the CIJ printer. Droplet A, with a charge of $-1.0 \times 10^{-13} \mathrm{C}$, enters at the midpoint between the plates at $20 \mathrm{~m} \mathrm{~s}^{-1}$ and is to be deflected upwards towards the piece of paper. Fig. 8.4 (not to scale) [1m]

Part 7: (i) Draw the electric field lines between the deflection plates on Fig. 8.4. [1m]

Part 8: (ii) Determine the electric field strength between the deflection plates. [2m]

Part 9: (iii) An engineer suggests using a magnetic field instead of an electric field to deflect droplet $A$. 1. Describe the direction of the magnetic flux density that is required to deflect droplet A upwards. [1m]

Part 10: 2. To deflect droplet A onto the paper, a reasonable radius of curvature for droplet A to undergo in the magnetic field would be 26.0 cm . By determining the magnitude of the magnetic flux density $B$ required to achieve a radius of curvature of 26.0 cm , comment on the feasibility of using a magnetic field in a commercial CIJ printer. Explain your working clearly. [3m]

Part 11: (c) In a thermal inkjet printer, a constant current of 0.50 A is passed through the thin-film resistor for a short time interval of $0.010 \mu \mathrm{s}$. This causes a square layer of ink below the thin-film resistor of thickness $x$ to heat up and vaporise. This is shown in Fig. 8.5. Fig. 8.5 [1m]

Part 12: (i) Determine the thermal energy produced by the current passing through the thin-film resistor. [2m]

Part 13: (ii) The ink in the ink chamber is initially at room temperature of $25^{\circ} \mathrm{C}$. Determine the maximum mass of ink that can be vaporised by the amount of thermal energy in (c)(i). [3m]

Part 14: (iii) Hence, determine the maximum thickness $x$ of the layer of ink that can be vaporised. $$ x=\quad \mu \mathrm{m} $$ [2m]

Part 15: (iv) Suggest a possible reason why the actual thickness of the vaporised layer in real thermal inkjet printers is much smaller than that calculated in (c)(iii). [2m]

Part 16: (d) State, with reference to the information given, an advantage and a disadvantage of thermal inkjet printing as compared to CIJ printing. Advantage: $\qquad$ Disadvantage: $\qquad$ [2m]

Back to Vault

Review

You're all caught up!

Similar Problems

OCR Extract
Mechanics
Particle A of mass $9 m$ and particle $B$ of mass $m$ travel towards each other along a smooth horizontal surface in a straight line and collide head-on. The initial speed of particle A before the collision is $u$. In Fig. 1.1, the variation with time $t$ of momentum $p$ is shown from $t=0$ to $t=3 T$ for particle $A$ and from $t=0$ to $t=T$ for particle $B. Fig. 1.1
OCR Extract
Mechanics
A uniform square box with sides 0.80 m and mass 2.0 kg is at rest on the ground. One end of a light rope is attached to the box and the other end is attached to the wheel of a motor. The motor applies a constant clockwise torque of 5.0 N m on the wheel of radius 0.20 m . At the instant shown in Fig. 2.1, the rope is taut and it makes an angle of $\theta=20^{\circ}$ with the vertical side of the box. The system remains in equilibrium. Fig. 2.1
OCR Extract
Mechanics
A bob of mass 1.5 kg is attached to a string of negligible mass and of length 25.0 cm . The other end of the string is fixed to point $X$ of an inverted " $L$ " structure of arm length $d$. The structure is fixed to the centre of a rotating disc of radius 8.0 cm . When the disc rotates with an angular velocity $\omega$, the string makes at an angle $\theta$ to the vertical as shown in Fig. 3.1. Fig. 3.1
OCR Extract
Mechanics
(a) Explain why gravitational potential is always negative whereas electric potential can have positive and negative values, given that both potentials are zero at infinity.
OCR Extract
Mechanics
(b) Fig. 4.1 shows how the gravitational potential $\phi$ from the surface of a planet varies with distance $r$ from the centre of the planet. Fig. 4.1
OCR Extract
Mechanics
A transverse wave on a rope is travelling to the right. Fig. 5.1 shows the waveform at a particular time. Particles Q, R, S, T, U and V are labelled. Fig. 5.1
OCR Extract
Mechanics
Fig 6.1 shows a miniature E10 filament light bulb with a rating of $6.0 \mathrm{~V}, 3.0 \mathrm{~W}$. Fig. 6.1
OCR Extract
Mechanics
A medical treatment makes use of a sample of americium-240 that emits alpha particles to kill cancer cells. In one such treatment, a total energy of 1140 J is applied to a tumour of mass 0.500 kg . At the start of the treatment, the mass of the americium-240 sample is $2.00 \times 10^{-9} \mathrm{~kg}$. Americium-240 has a half-life of 50.2 hours, and it decays by emitting an alpha particle of kinetic energy 5.71 MeV .