Do you lose weight when you reach the top of the mountain? If you carry a weighing machine with you, you will probably be so happy that you weigh lighter when you reach the top of the mountain.

The following is a past year question from GCE “O” Level Physics (6091) in the year Nov 2014. Try it and see for yourself.

Examination Question (GCE “O” Level Physics (6091) -Nov 2014/P1/Q9)

A person of weight 600N at the bottom of a mountain climbs to the top. The gravitational field strength changes from 9.81N/kg at the bottom to 9.79N/kg at the top. His mass is unchanged as he climbs.

What are his mass and his weight at the top of the mountain?

| Mass at top of mountain/ kg | Weight at top of mountain / N |

A | 61.2 | 599 |

B | 61.2 | 600 |

C | 61.3 | 599 |

D | 61.3 | 600 |

Solution

The first thing we need to find out is the mass of the person. We are told that his weight is 600N at the bottom of the mountain.

So his mass can be computed as follows:

Mass = 600 / 9.81 =61.16 kg ≈ 61.2kg

Since the gravitational field strength at the top of the mountain is 9.79 N/kg, then the weight of that person at the top of the mountain is:

Weight = 61.16 x 9.79 = 598.78 kg ≈599kg

So the answer is A.

Explanation and Key Concepts

Gravitational field strength of a planet is the gravitational force acting on per unit mass of an object due to the gravity of the planet. The gravitational field strength is the strongest on the surface of the planet and it gets weaker as you move away from the surface.

The weight of an object is the force exerted by the planet on that object as a result of this force of gravity. Hence the weight of an object is given by :

Weight = mass x gravitational field strength

The mass of an object is the amount of substance in that object. It is dependent on the amount of atoms and molecules in that object. It is not dependent on the gravitational pull of the planet. Hence, regardless of where that object is, its mass remain unchanged. So that person’s mass remain the same whether he is at the top or at the bottom of the mountain.

However, his weight will change because the gravitational field strength gets weaker as he moves away from the surface of the earth towards the top of the mountain.

Conclusion

Do you weigh lighter when you reach the top of a mountain? Well, when you reach the top of the mountain, whether you lose water through perspiration or whether you gain in muscle mass through the climbing, the fact is, if all things remain unchanged, i.e. if the atoms and molecules inside you remain unchanged, you will still weigh lighter because the gravitational pull on you is lesser at the top of the mountain.