Question

There’s life on Zoopledorf! While on a routine patrol in your spacecraft outside the planet, you and your colleague Captain Clark (who is traveling in her own completely separate ship) encounter an unknown spacecraft, presumably crewed by Zoopledorfians. Apparently spotting you as well, the strange ship accelerates away, and you take this as an opportunity to learn more about its technological capabilities. Specifically, you measure the ship’s acceleration in order to determine the force its engine can exert. Using your own ship’s scanning tools, you measure the UFO’s acceleration to be a =1200 m/s 2. You report this value to Captain Clark, who responds that she has measured a'= 1150 m/s2 instead. Clearly something is wrong here, since the force the spacecraft exerts has some definite value, but your measurements suggest two different values for this force, either Fship =mship.a or F'ship=m' ship.a. (The numbers here are actually irrelevant, the only thing that matters is that they’re different from one another.)

Before you can diagnose what went wrong, all of your ship’s scanners and meters are jammed, apparently by the Zoopledorfian craft. You can’t even tell if your ship’s engines are on! Fortunately, in a flash of inspiration, you figure out a way you can tell which of the two measurements for the acceleration was correct. (You can assume for this problem that either you or Captain Clark measured the true value of the force exerted by the ship.) All of your ship’s electronics are shut down (including the controls for the window shutters, which are closed tight), and there’s no free-standing equipment on the ship, but you did coincidentally bring the ball that you used for the last experiment in your space suit pocket.

Explain a simple experiment you can conduct using only the ball and your senses to determine whether you measured the true acceleration of the ship. You should explain what the outcome of the experiment will be — what will happen to the ball — if you did measure the true value, and what happens to the ball if you didn’t measure the true value. Assume your own ship is moving exactly as it was when you measured the acceleration, and assume there are no gravitational or other forces on your ship except for potentially the force exerted by the engines. (Remember, you don’t know if the engines are on or off.) This also means you should assume no gravitational force acts on the ball. Don’t think too hard about this. It is really simple.

Answer 1

If we assume that one of the measurements of acceleration are correct, one of them is non-inertial frame with it's own acceleration.

if your own frame is accelerating , the moment you let go the ball from your hand , it will stop accelerating but your space ship wil be accelerating and hence ball will be accelerating towards or away from end of space ship.

In case this does not happen you can decide your frame is inertial and hence your measurement of acceleration is correct.