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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 determine the motion of gear R, we consider the gear ratios. Gear P has 10 teeth and gear R has 40 teeth. Since gear R is larger, it will turn slower than gear P. The rotation speed of gear R can be calculated using the formula for gear ratios:
ext{Speed ratio} = rac{ ext{Number of teeth on R}}{ ext{Number of teeth on P}} = rac{40}{10} = 4
Thus, if gear P completes 1 revolution, gear R completes: ext{Speed of R} = rac{1}{4} ext{ revolutions per second}
This means gear R rotates in the opposite direction to gear P since gears turn in opposite directions when interlocked. The correct answer is option C, which states that gear R has a speed of 1 revolution per second and moves opposite to P.
Step 2
Calculate how far the rack moves when P turns through one complete revolution.
Answer
When gear P turns through one complete revolution, it moves the rack a distance dependent on the circumference of gear P. The circumference (C) can be found using:
Given that gear P has 10 teeth and each tooth is 2 mm apart, we compute:
Since gear P makes one complete revolution, the rack moves 20 mm. Therefore, the answer is: distance = 20 mm.
Step 3
Use the principle of moments to calculate the mass of the toy elephant.
Answer
In order to find the mass of the toy elephant, we apply the principle of moments about the pivot point of the rod, which states that the total clockwise moments must equal the total anticlockwise moments.
Calculating the clockwise moment due to the elephant and the rabbit:
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The moment due to the elephant (mass = m, distance from pivot = 17 cm) is:
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The moment due to the rabbit (mass = 6 g, distance from pivot = 15 cm) is:
This must equal the moment due to the second rabbit (mass = 4.6 g, distance from pivot = 10 cm):
Setting up the equation:
Solving for m gives: m = rac{(6 imes 15) + (4.6 imes 10)}{17}
Calculating:
ightarrow m = rac{136}{17} ightarrow m = 8 ext{ g}$$ Thus, the mass of the toy elephant is 8.0 g.Step 4
Explain the difference between the size of force K and the size of force L.
Answer
The force exerted by piston Y (force K) and the force exerted by piston Z (force L) is based on Pascal's principle, which states that pressure in a contained fluid is transmitted equally in all directions. The formula for pressure (P) can be noted as:
P = rac{F}{A}
Where F is the force applied and A is the area. Since the area of piston Y is less than the area of piston Z, the forces will differ. Therefore,
- The pressure exerted on piston Y is equal to the pressure exerted on piston Z: rac{F_K}{A_Y} = rac{F_L}{A_Z}
From this, we conclude:
Since , it follows that . Thus, the force K is less than force L.