Modelling assumptions and limitations

A question is this type if and only if you must state, explain, or critique modelling assumptions such as particle model, air resistance, or constant gravity.

3 questions · Moderate -0.7

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AQA M1 2005 June Q5
7 marks Moderate -0.5
5 A sphere of mass 200 grams is released from rest and allowed to fall vertically.
  1. A student states that the acceleration of the sphere is \(9.8 \mathrm {~ms} ^ { - 2 }\) while it is falling. What modelling assumption is this student making?
  2. The student conducts an experiment and finds that the acceleration of the ball is in fact \(8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). He formulates a model for the motion that assumes a constant resistance force acts on the ball as it is falling.
    1. Calculate the magnitude of this resistance force based on this assumption.
    2. Describe how the resistance force would vary in reality.
  3. In a revised model the resistance force is assumed to be proportional to the speed of the sphere.
    1. State the initial acceleration of the sphere.
    2. State what would happen to the acceleration of the sphere if it were able to fall for a long period of time.
Edexcel M1 Q1
5 marks Easy -1.2
  1. A golf ball and a table tennis ball are dropped together from the top of a building. The golf ball hits the ground after 1.7 seconds.
    1. Calculate the height of the top of the building above the ground.
    According to a simple model, the two balls hit the ground at the same time.
  2. State why this may not be true in practice and describe a refinement to the model which could lead to a more realistic solution.
AQA AS Paper 1 2023 June Q14
4 marks Moderate -0.3
A ball, initially at rest, is dropped from a vertical height of \(h\) metres above the Earth's surface. After 4 seconds the ball's height above the Earth's surface is \(0.2h\) metres.
  1. Assuming air resistance can be ignored, show that $$h = 10g$$ [3 marks]
  2. Assuming air resistance cannot be ignored, explain the effect that this would have on the value of \(h\) in part (a). [1 mark]