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Figure 10 shows an arrangement of gears - Edexcel - GCSE Physics - Question 6 - 2018 - Paper 1
Question 6
Figure 10 shows an arrangement of gears. Each gear turns around a fixed axle. Gear P is turned through one complete revolution per second. Which of the following de... show full transcript
Worked Solution & Example Answer:Figure 10 shows an arrangement of gears - Edexcel - GCSE Physics - Question 6 - 2018 - Paper 1
Step 1
Which of the following describes the motion of gear R?
Answer
To solve this, we first analyze the gear ratios. Gear P has 40 teeth and gear R has 20 teeth. When gear P makes one complete revolution, gear R will rotate as follows:
Using the gear ratio: [ \text{Gear Ratio} = \frac{\text{Teeth of P}}{\text{Teeth of R}} = \frac{40}{20} = 2 ]
This means that for every revolution of gear P, gear R turns 2 revolutions. Moreover, the direction of rotation will be opposite to that of gear P.
Thus, the correct answer is C: ( \text{speed (revolutions per second)} = 2, \text{direction of rotation} = \text{opposite to P} ).
Step 2
Calculate how far the rack moves when P turns through one complete revolution.
Answer
To find out how far the rack moves, we use the number of teeth on gear P (10 teeth) and gear Q (40 teeth). Each complete revolution of gear P moves the rack through the distance of the teeth on gear Q.
The distance moved can be calculated as follows:
- Gear P turns completely: 1 revolution moves the gear Q by its circumference.
- The gear ratio between P and Q is: [ \text{Gear Ratio} = \frac{10}{40} = \frac{1}{4} ]
The distance moved by the rack for 1 revolution of gear P: [ \text{Distance} = \text{Circumference of gear P} \times \left(\frac{\text{Teeth of P}}{\text{Teeth of Q}}\right) ]
distance = 2 mm (as there are 2 mm between the teeth on the rack). Thus, the distance moved by the rack is 10 mm.
Step 3
Use the principle of moments to calculate the mass of the toy elephant.
Answer
We will use the principle of moments about the point where the rod is attached to the ceiling.
Taking moments about the center:
- Moment due to the elephant: ( \text{mass} \times g \times 10cm )
- Moment due to the rabbit: (6.0g \times g \times 15 cm)
- Moment due to the other animal: (4.6g \times g \times 17cm)
Setting up the equation: [ m \times 17 = (6.0 \times 15) + (4.6 \times 10) ]
Solving for m, we get: [ m = \frac{90 + 46}{17} = 8 g ]
Thus, the mass of the toy elephant is 8.0 g.
Step 4
Explain the relationship between the size of force K and the size of force L.
Answer
To understand the relationship between force K and force L, we can use the principle of hydraulics.
Since the area of piston Y is less than the area of piston Z, we can express the pressures: [ P = \frac{F}{A} ]
Thus, the pressure exerted on piston Y should equal that on piston Z.
- This indicates that force K (on piston Y) must be less than force L (on piston Z).
In summary, because the area of piston Z is greater, the force required to balance the system under the same pressure conditions varies, making force K less than force L.