Relativity

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Question 5 in the 2003 HSC Physics examination was a multiple choice question on time dilation and length contraction. Unfortunately, no correct answer was given as an alternative. Students doing revision often ask about this question. As the mark for the question was apparently not included in the final mark it could probably be ignored. However, an answer involves taking into account the travel time of the light coming from the Earth as the question says "when seen from the astronaut's spaceship"...seen implying making an observation using light .  From the point of view of the astronaut in the spaceship the Earth is moving away at 0.8c. The time for the journey in the reference frame of the spaceship is 10 years. The distance of the journey in the reference frame of the spaceship is 8 light years and so a ray of light would take a time interval of 2 years in the spaceships reference frame to reach the spaceship. To determine the corresponding time interval shown by the clock on the Earth we solve the time dilation equation for t0 putting tv as 2 and v as 0.8c. This is because the astronaut considers the Earth to be moving away carrying its clock with it. This works out to be 1.2 years.

 

Simple Pendulum

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The simple pendulum is one of the oldest Physics demonstrations and examination questions. A simple pendulum consists of a mass tied to one end of a string, the other end of which is fixed, and the mass is allowed to swing freely in a vertical plane. The important physical concept involved is energy. At any point of its motion the energy (meaning the "total" energy) of the pendulum is constant, provided frictional forces are negligible. Energy is said to be a constant of the motion. In Physics problems we always look for constants. Constants allow us to determine many properties of the motion of a system. Here is a list of some pendulum problems that students usually find difficult.

  1. Determine the magnitude of the acceleration of the mass when it is at the lowest point of its swing. Is it zero? Is it g?
  2. What is the direction of the acceleration vector of the mass at the lowest point of its swing?
  3. Determine the magnitude of the acceleration of the mass at the highest point of its swing. Is it zero?
  4. Imagine that a simple pendulum of mass m and length L is set moving so that it just reaches the vertical position over the point of support. Determine the energy of the pendulum in terms of g, L and m. Neglect frictional forces.[2.5mgL]
  5. Imagine that the mass is set moving and the string becomes slack before it reaches the vertical position. The mass then falls on a path that passes through the point of support. Determine the energy of the mass in this situation in terms of g, L and m. Neglect friction forces. [1.86603mgL]
  6. As in question 5 but now the path of the falling mass passes through the lowest point of the swing of the pendulum.[1.75mgL]
  7. As in question 5 but now the path of the falling mass passes through the horizontal through the point of support at a distance L from the point of support. [2.29904mgL]