You are part of a team that has been sent to the South Pole for experiments on the acceleration of gravity in extreme latitudes. After some initial thoughts, you presented the idea of using a conical pendulum. One member of the team asked how this experiment could be used to determine the gravitational pull at the location. You replied stating that, for small angles of oscillation, the conical pendulum executes a simple harmonic motion.

• DERIVE is the expression for the period of oscillation of the simple conical pendulum. Use cos θ = 1 Don’t forget to include a free-body diagram.
  EXPLAIN, from the obtained model, how gravity can be estimated.

 

• Your team, then, leaves the shelter and goes to the middle of an ice plateau. There is a frame, from whose top a steel wire is stretched, and its free end is attached to a tennis ball. After carrying out the experiment, you notice that the value calculated for the acceleration of gravity is considerably larger than expected. In a preliminary experiment, carried out inside the shed and with a metallic sphere, the value found for gravity was acceptable. Upon deliberating on what happened, some members of the team proposed explanations to you