View the video on how the gauge works.
As the fuel level drops, the float which stays on the fuel surface will descend. The rod which is attached to the float will turn clockwise about the pivot X. As the rod turns, the resistance on the variable resistor increases. This increases the resistance of the circuit. Hence the current flowing through the circuit will decreases, causing the needle to deflect more to the left, indicating towards E (empty). Thus the reading on the fuel gauge decreases.
(i) Both the fixed resistor and sensor are in series.
Total effective resistance Re = 5000 + 1000 = 6000 ohms
V = IR
12 = I x 6000
I = 0.0020 A
Hence potential across Y, V = IR (where I is constant in a series circuit)
= 0.0020 x 1000
= 2.0 V
(ii) When the temperature increases and the resistance of sensor Y decreases, the total effective resistance of the circuit decreases. Current flowing through the circuit increases.
Since V = IR, where the R of the fixed resistor is a constant 5000 ohms, as current I increases, the potential difference across the 5000 ohms resistor will increase.
When a system is in equilibrium, 2 conditions are met.
1) Principle of Moment (POM):
Sum of anticlockwise moment = Sum of clockwise moment
2) Net force = 0N; all forces are balanced:
Total downward forces = Total upward forces
Whenever a force passed through the pivot point, that force will not create any moment as there is no perpendicular distance from the force to the pivot. Hence this force will not be included in the calculation of moments.
(a) (i) A bigger force than F can be obtained due to the level system and hydraulic system.
Level system: Applying principle of moments, the anticlockwise moment by the F is equal to the clockwise moment by the force on piston A (note that the handle is pushing the piston down, but the piston A is pushing on the handle upwards – action = reaction). As the perpendicular distance from F to the pivot is greater than the perpendicular distance of the force by piston to the pivot, the force on the piston A is greater than F at handle.
Hydraulic system: As the pressure transmitted in the liquid is the same, pressure at piston A = pressure at piston B. As P = F/A and area of piston A is smaller than area of piston B, a larger force is obtained in piston B.
Hence these two systems allow the force on piston B to be greater than F at the handle.
(a) (ii) Both liquid and gas molecules are in a continuously random motion. But in liquid, the molecules are closely packed together and able to slide around one another. There is very little empty space between the molecules hence liquid is not compressible. Gas molecules are far apart from one another, hence gas can be easily compressed.
(b) P = F/A = 12000 / 0.060 = 200 000 Pa
(c) Velocity is the vector quantity while speed is a scalar. As the car goes round the bend, the direction of the car changes. Hence velocity is changing even though speed is constant.
Likewise, as the velocity is changing, the car is considered to have an acceleration (not in the sense of increasing speed though).
Centre of gravity (CG) is the point where the whole weight of the object seems to act.
Weight acts from the CG vertically down.
If the object is pivoted at the cg, the weight of the object, which acts vertically downwards from the cg, does not create any moment about the pivot point. As M = F x d, there is no perpendicular distance from the weight to the pivot.