13 There are four forces acting on an aeroplane in flight, as shown. (a) The lift force is perpendicular to the wings. To change direction, the aeroplane 'banks' so that one wing is lower than the other wing. The lift force is then no longer vertical. The aeroplane flies in a horizontal circular path at a speed of 52ms⁻¹. The diagram below shows the aeroplane banking at an angle of 20° to the horizontal. (i) Show that the radius of the circular path is about 800 m. mass of aeroplane = 1200 kg speed of aeroplane = 54 ms⁻¹ (ii) Determine the time taken by the plane to move through 90° of the circular path. speed of aeroplane = 54 ms⁻¹ (b) The wings of the aeroplane are now levelled, as shown below. The speed and the magnitude of the lift force remain the same. Explain what will happen to the vertical motion of the aeroplane. (Total for Question 13 = 9 marks)

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13 There are four forces acting on an aeroplane in flight, as shown - Edexcel - A-Level Physics - Question 13 - 2023 - Paper 4

Question 13

13 There are four forces acting on an aeroplane in flight, as shown. (a) The lift force is perpendicular to the wings. To change direction, the aeroplane 'banks' so ... show full transcript

Worked Solution & Example Answer:13 There are four forces acting on an aeroplane in flight, as shown - Edexcel - A-Level Physics - Question 13 - 2023 - Paper 4

Step 1

(a)(i) Show that the radius of the circular path is about 800 m.

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Answer

To determine the radius of the circular path, we first calculate the weight of the aeroplane.

We use the formula:

$W = mg$

Substituting the values:

$W = 1200 ext{ kg} imes 9.81 ext{ m/s}^2 = 11772 ext{ N}$

Next, we resolve the vertical component of the lift force, which is acting at a 20° angle. The vertical component is:

$L_{ ext{vertical}} = L imes ext{cos}(20°)$

Given that the lift force must equal the weight of the aeroplane:

$L_{ ext{vertical}} = W$

Thus:

$L imes ext{cos}(20°) = 11772 \ ext{N}$

To find the lift force, we need to use centrifugal force, where:

$F_c = rac{mv^2}{r}$

Setting the centripetal force equal to the lift force:

$L_{ ext{horizontal}} = rac{1200 ext{ kg} imes (54 ext{ ms}^{-1})^2}{r}$

Combining both components,

Using trigonometry we find:

$L_{ ext{horizontal}} = L imes ext{sin}(20°)$

After calculation, we find:

$r = rac{1200 ext{ kg} imes 54^2 ext{ m/s}^{-2}}{4285 ext{ N}} \ ext{and thus} \ r ext{ is approximately } 800 ext{ m}$ .

Step 2

(a)(ii) Determine the time taken by the plane to move through 90° of the circular path.

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Answer

To find the time taken to travel through 90° of the circular path, we first find the circumference of the circular path:

$C = 2 ext{π}r$

Substituting in our previously calculated radius:

$C = 2 imes ext{π} imes 800 ext{ m} \\ C ext{ is approximately } 5026.55 ext{ m}$

Now, the distance for 90° is:

$rac{C}{4} = rac{5026.55}{4} = 1256.64 ext{ m}$

Next, using the speed of the aeroplane:

$ext{time} = rac{ ext{distance}}{ ext{speed}}$

Substituting the values:

$t = rac{1256.64 ext{ m}}{54 ext{ ms}^{-1}} = 23.28 ext{ seconds}$ .

Step 3

(b) Explain what will happen to the vertical motion of the aeroplane.

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Answer

When the wings of the aeroplane are levelled, the vertical component of the lift force will align directly with the vertical.

In this scenario, if the lift force still exceeds the weight of the aeroplane, the aeroplane will accelerate upwards. Conversely, if the lift is equal to the weight, the aeroplane will maintain a steady altitude. However, since both speed and lift magnitude remain unchanged, the aeroplane will likely ascend unless otherwise noted.

13 There are four forces acting on an aeroplane in flight, as shown - Edexcel - A-Level Physics - Question 13 - 2023 - Paper 4

Worked Solution & Example Answer:13 There are four forces acting on an aeroplane in flight, as shown - Edexcel - A-Level Physics - Question 13 - 2023 - Paper 4

(a)(i) Show that the radius of the circular path is about 800 m.

(a)(ii) Determine the time taken by the plane to move through 90° of the circular path.

(b) Explain what will happen to the vertical motion of the aeroplane.

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