Estimating physical quantitiesAQA A-Level Physics: Subtopic test

1. 1
   A teacher asks a class to estimate the sizes and masses of familiar objects and particles to the nearest order of magnitude.

   (a)

   What is the mass of a typical family car, to the nearest order of magnitude?

   [1 mark]

   • A10⁰ kg
   • B10¹ kg
   • C10² kg
   • D10³ kg

   (b)

   What is the diameter of a typical atom, to the nearest order of magnitude?

   [1 mark]

   • A10⁻⁶ m
   • B10⁻⁸ m
   • C10⁻¹⁰ m
   • D10⁻¹⁴ m

   (c)

   A nucleus has a diameter of order 10⁻¹⁵ m and an atom has a diameter of order 10⁻¹⁰ m. Estimate how many times larger the volume of the atom is than the volume of its nucleus.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student estimates the number of times a human heart beats in a lifetime. Assume a resting heart rate of about 70 beats per minute and a lifetime of about 80 years.

   (a)

   What is the number of seconds in 80 years, to the nearest order of magnitude?

   [1 mark]

   • A10⁸
   • B10⁹
   • C10¹⁰
   • D10¹¹

   (b)

   What is the number of heartbeats in a lifetime, to the nearest order of magnitude?

   [1 mark]

   • A10⁹
   • B10⁷
   • C10¹¹
   • D10¹³

   (c)

   Each heartbeat pumps about 70 cm³ of blood. Estimate the total volume of blood pumped in a lifetime, in m³, to the nearest order of magnitude.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A classroom is about 10 m long, 8 m wide and 3 m high. The density of air is about 1.2 kg m⁻³, the molar mass of air is about 0.029 kg mol⁻¹ and the Avogadro constant is 6.0×10²³ mol⁻¹.

   (a)

   Estimate the mass of air in the classroom, to the nearest order of magnitude.

   [3 marks]

   (b)

   Estimate the number of molecules of air in the classroom, to the nearest order of magnitude.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A typical family car has a mass of about 1.2×10³ kg and travels at about 30 m s⁻¹ on a motorway. A typical AA battery stores about 1×10⁴ J of energy, and a typical car engine can deliver a maximum power of about 7×10⁴ W.

   (a)

   Estimate the kinetic energy of the car, and the number of AA batteries that store the same amount of energy, each to the nearest order of magnitude.

   [6 marks]

   (b)

   The car accelerates from rest to 30 m s⁻¹ in about 10 s. Estimate the average power needed to do this, to the nearest order of magnitude, and evaluate whether the engine could provide it.

   [6 marks]

   Total for question 4: 12 marks

End of questions