# You are in a rocket accelerating upward relating to Earth at 2g. If you were on a scale, how...

## Question:

You are in a rocket accelerating upward relating to Earth at {eq}2g {/eq}. If you were on a scale, how would the reading compare to your normal weight?

• (a) Two times normal
• (b) Three times normal
• (c) Same as normal
• (d) Zero

## Apparent Weight:

Ordinary weighing scales actually measure your weight and not your mass. The machines rely on the fairly definite correspondence between weight and mass near the Earth's surface as given by g. A useful thought experiment to drive the point home is that your scale reading when aboard the international space station is zero i.e. there is no normal reaction to your weight from the scale. In fact, ideally, depending on your motion state, your scale reading can range anywhere from zero to infinite.

When you are in a rocket accelerating upwards, the scenario is not different from being in an elevator accelerating upwards.

In fact, you can just think back to the last time when you were in an elevator and the elevator just started moving: For the first few moments when the elevator is building up its speed, you feel heavier.

This is because the normal reaction of the elevator floor on you (which is responsible for the sensation of weight) equals your rest weight and the acceleration force on your body.

By a logical extension, for a rocket moving upwards at 2g, your acceleration force on you would be 2mg where m is your mass.

Your weight would thus be your normal weight mg plus the acceleration force 2mg on your body. This gives 3mg i.e. three times your normal weight.

 As such, when you are in a rocket accelerating at 2g, your weight would be (b) three times normal. Practice Applying Newton's Third Law

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Chapter 17 / Lesson 10
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Newton's Third Law, which relates action and reaction, can be applied to many different scenarios in physics and in real life. Look into the definition of Newton's Third Law, then explore some examples to practice applying it.