You are assigned the task of designing an accelerometer to be used inside a rocket ship in outer space. Your equipment consists of a very light spring that is 15.0 cm long when no forces act to stretch or compress it, plus a 1.10 kg weight. One end of this spring will be attached to a friction-free tabletop, while the 1.10 kg weight is attached to the other end, as shown in the figure. (Such a spring-type accelerometer system was actually used in the ill-fated Genesis Mission, which collected particles of the solar wind. Unfortunately, because it was installed backwards, it did not measure the acceleration correctly during the craft's descent to earth. As a result, the parachute failed to open and the capsule crashed on Sept. 8, 2004.)
A.) What should be the force constant of the spring so that it will stretch by 1.10 cm when the rocket accelerates forward at 2.50 m/s^2? Start with a free-body diagram of the weight.
B.)What is the magnitude of acceleration of the rocket if the spring is compressed by 2.30 cm?
C.)What is the direction of acceleration of the rocket if the spring is compressed by 2.30 cm (Forward or Backward)?