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GCSE Questions: Energy Changes

Q11. The diagram shows Peter launching a toy aeroplane.

To launch the aeroplane, Peter pulls on it to stretch the spring and then releases it.

(a) Just before the toy aeroplane is released, the spring has an extension of 0.12 m.

Given that the mass of the aeroplane is 0.020 kg and the spring constant of the spring is 50 N/m, calculate the maximum speed of the toy aeroplane just after it is launched.

Force applied to the spring = ke

Energy stored by the spring = ½Fe = ½ke2

Es = ½ x 50 x 0.122

Es = 0.36 J

Energy gained is turned into kinetic energy of the toy aeroplane:

Ek = ½mv2

0.36 = ½ x 0.020 x v2

v2 = 0.36 x 2/0.020 = 36

v = 6.0 m/s

Alternative approach:

F = ke

F maximum = 50 × 0.12

F = 6.0 N

F = ma

6.0 = 0.020 × a

Maximum a = 300 m/s2

Mean a = 150 m/s2

v 2 – u 2 = 2as

v2 = 2 × 150 × 0.12 = 36

v = 6.0 m/s

[6 marks]

(b) Complete the sentence:

As the aeroplane moves upwards through the air there is a decrease in the kinetic energy of the aeroplane.

[1 mark]

(c) Give one factor which would increase the distance the toy aeroplane travels horizontally before hitting the ground.

increasing the extension of the spring giving it more elastic potential energy

or

increase the angle of release (to the horizontal by a small amount)

[1 mark]

[Total 8 marks]