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PHYSICS, M2 EQ-Bank 13

An 80 kilogram astronaut in deep space (far from any significant gravitational field) throws a 2.0 kg toolbox away from their spacecraft with a force of 10 N applied for 2.0 seconds.

  1. Explain what happens to the astronaut as a result of this action.   (2 marks)
  1. Explain why the accelerations of the astronaut and the toolbox are different in terms of their inertia, despite experiencing forces of equal magnitude.   (3 marks)
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a.    Due to Newton’s Third Law:

  • The toolbox exerts an equal and opposite force (10 N) on the astronaut.
  • This causes the astronaut to accelerate in the opposite direction of the throw with an acceleration of \(0.125\ \text{ms}^{-2}\).
  • After the 2 seconds, the astronaut will continue moving at constant velocity in opposite directions as there is no longer any force acting back on the astronaut (Newton’s First Law).

b.   Reasons accelerations differ:

  • Although the astronaut and the toolbox experience equal and opposite forces (10 N), as required by Newton’s Third Law, their accelerations differ because of their different inertia.
  • Inertia is an object’s resistance to changes in its motion, and it depends directly on mass. The astronaut has much greater mass (80 kg) than the toolbox (2.0 kg), meaning the astronaut has greater inertia. Therefore the astronaut will be more resistant to a change in motion and will experience a smaller acceleration.
  • By applying Newton’s second law \(F=ma\), the acceleration of the astronaut is \(0.125\ \text{ms}^{-2}\) whereas the acceleration of the tool box is \(5\ \text{ms}^{-2}\).
Show Worked Solution

a.    Due to Newton’s Third Law:

  • The toolbox exerts an equal and opposite force (10 N) on the astronaut.
  • This causes the astronaut to accelerate in the opposite direction of the throw with an acceleration of \(0.125\ \text{ms}^{-2}\).
  • After the 2 seconds, the astronaut will continue moving at constant velocity in opposite directions as there is no longer any force acting back on the astronaut (Newton’s First Law).

b.   Reasons accelerations differ:

  • Although the astronaut and the toolbox experience equal and opposite forces (10 N), as required by Newton’s Third Law, their accelerations differ because of their different inertia.
  • Inertia is an object’s resistance to changes in its motion, and it depends directly on mass. The astronaut has much greater mass (80 kg) than the toolbox (2.0 kg), meaning the astronaut has greater inertia. Therefore the astronaut will be more resistant to a change in motion and will experience a smaller acceleration.
  • By applying Newton’s second law \(F=ma\), the acceleration of the astronaut is \(0.125\ \text{ms}^{-2}\) whereas the acceleration of the tool box is \(5\ \text{ms}^{-2}\).