An engineer uses a single optical sensor to measure the speed of packages sliding down a straight conveyor chute in an automated warehouse. A thin rectangular label of known length is attached to the top of each package to trigger the optical sensor as it passes.
Which two measurements are required to determine the speed of the package as it passes the optical sensor? (Choose two from: Total mass of the package, Length of the label, Duration for which the optical beam is broken by the label, Angle of inclination of the chute, Total length of the chute.)
A test capsule is dropped down a vertical, evacuated drop-shaft of a pneumatic transport system. The decrease in the gravitational potential energy of the capsule during the descent is 17.64 kJ17.64\text{ kJ}17.64 kJ. The capsule descends through a vertical height of 25.0 m25.0\text{ m}25.0 m. Taking the gravitational field strength g=9.8 N/kgg = 9.8\text{ N/kg}g=9.8 N/kg, calculate the mass of the capsule.
Assuming air resistance and other resistive forces inside the evacuated drop-shaft are completely negligible, explain why capsules of different masses reach the bottom of the shaft with approximately the same speed when dropped from the same height.