4-2 Suppose that you step onto an elevator. The doors shut and there are no windows. You notice that next to you is Albert Einstein. He is standing on a scale that reads his weight, 145 lbs Einstein speaks: "The scale reads my weight due to the force of gravity, BUT! – Since there are no windows on the elevator it would be impossible for us to tell the difference between standing on a scale in the presence of the earth’s gravitational field, OR being out in space with no gravitational force on us at all, but accelerating. You see, accelerations produce forces just like gravitational fields do, and inside this elevator it would be impossible to do any experiment to tell whether the force that I read on this scale below me is due to gravity or acceleration. I call this the equivalence principle. It is part of my theory of general relativity."

Einstein then hits the button for the 25^th floor. The elevator begins to move upward. The scale now reads 165 lbs "See, the acceleration of the elevator is now causing a greater force to be read by the scale. But soon the elevator will reach a constant velocity." As the elevator reaches a constant velocity the reading on the scale returns to 145 lbs. As the elevator slows, the scale reads 125 lbs. The elevator then stops at the 25^th floor and the doors open. As Einstein exits he says, "As an exercise you should calculate the curvature of space-time produced by the gravitational field of the earth. In addition, you can also calculate the acceleration of the elevator as we moved upward earlier." He then vanishes into thin air.

Solution: The first part of Einstein’s question is better left to the weirdos taking general relativity. As for the second part, we know that Einstein’s apparent weight increased by 20 lbs when the elevator accelerated upward. Let’s convert this to Newtons:

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We know the force on Einstein produced by the elevator. What we need now is his mass. Then we can use F = ma to get the acceleration of the elevator. To get Einstein’s mass we can use the fact that we know his weight at rest. Let’s get that in Newtons:

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Now to find his mass:

So the acceleration of the elevator (which is the same as Einstein’s acceleration since they are not moving relative to each other) is the force on Einstein divided by his mass, or

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