[Guest]

You are in an office on the 10th floor of a building. It is 3 am on quiet summer night. There are ten bags filled with lots of gold coins. One of the bags is filled with faked gold coins. They are identical to the real ones except they weigh slightly more. You may not leave the office until you find three ways (at least) to determine which bag had fake gold coins.

assume normal office supplies, MacGyver.

* oh the scale you had planned use is broken.

** as a rookie not sure if this truely constitutes a puzzle but I hope it is of some interest.

[Guest]

I am not sure I understand your point. In presence of significant air resistance (drag) the heavier object will fall faster than the lighter object of the same shape.

Take a large coin and cut out an identical shape from a piece of Styrofoam. Drop them from the same height at the same time and observe.

Force of gravitational attraction is directly proportional to the mass of the object. F = mg, where acceleration constant g = 9.8 m/sec². In the absence of air resistance, the objects fall at the same rate (increase in attraction force being cancelled by the increase in mass g = F/m). However, it would take proportionally smaller drag force to negate gravitational attraction and reach its terminal velocity for the lighter object. In other words, while the drag force is the same for the identical shape objects moving at the same speed, smaller force is required to stop lighter object’s acceleration.

Thanks for the comments and explanation. My understanding is the heavier object may only fall faster because its terminal velocity will be higher. Identical objects of un-equal mass fall at the same rate until one reaches terminal velocity and then the other heavier one over takes it. I do not think there is any difference in their velocities during the acceleration period. In your example of a styrofoam coin it quickly reaches terminal velocity however in this puzzle I doubt that becomes a factor as a 30 m drop would only allow a max velocity of 24 m/s.

Let me know if this does not appear to be consistent with the laws of physics.

[Prime]

Thanks for the comments and explanation. My understanding is the heavier object may only fall faster because its terminal velocity will be higher. Identical objects of un-equal mass fall at the same rate until one reaches terminal velocity and then the other heavier one over takes it. I do not think there is any difference in their velocities during the acceleration period. In your example of a styrofoam coin it quickly reaches terminal velocity however in this puzzle I doubt that becomes a factor as a 30 m drop would only allow a max velocity of 24 m/s.

Let me know if this does not appear to be consistent with the laws of physics.

The lighter object will fall behind at all times.

Consider 10 kg object and 2 kg object. Both start falling with acceleration 9.8 m/sec². Say, at some speed V, the drag force is 9.8 kg*m/sec², which only depends on the object shape and speed. At that point the total force acting on the 2 kg object is only half of the initial gravitational force. The total force acting upon 10 kg object is 0.9 of its gravitational attraction. Thus the 2 kg object accelerates at 4.9 m/sec² at that point and the 10 kg object accelerates at approx. 8.8 m/sec².

[Guest]

The lighter object will fall behind at all times.

Consider 10 kg object and 2 kg object. Both start falling with acceleration 9.8 m/sec². Say, at some speed V, the drag force is 9.8 kg*m/sec², which only depends on the object shape and speed. At that point the total force acting on the 2 kg object is only half of the initial gravitational force. The total force acting upon 10 kg object is 0.9 of its gravitational attraction. Thus the 2 kg object accelerates at 4.9 m/sec² at that point and the 10 kg object accelerates at approx. 8.8 m/sec².

Thanks Prime! I have a much better understanding of the concept now, and I am reprogramming my brain to accommodate this.