PSLE Science TOTW ~ Is Gravitational Force Constant?


One of the questions that frequently trip students up is whether gravitational force acting on a body is constant regardless of position. For example, is the gravitational force acting on Stephy the same whether she is standing at Toa Payoh or when it she is balancing herself atop the summit of Mount Everest?

For Primary School syllabus, discussions about gravity are limited to the 'earthly' level. So the only context we need to be concerned with is Earth's gravitational pull on a body on Earth. By definition, the weight of an object on Earth is the gravitational force acting on the object. (Strictly speaking, it is the gravitational force they mutually exert on each other, but since Earth is a lot more massive than the objects on it, we can simply think of the pull as being one-way for simplicity.)

The question then becomes this: is Stephy's weight different when she's at Toa Payoh and when she's on top of Mount Everest?

To answer this, we'll need to make use of (Sir) Isaac Newton's Law of Universal Gravitation. Published in 1687, this law states that the gravitational force (F) between 2 bodies is directly proportional to the product of their masses (m1, m2) and inversely proportional to the square of the distance (r) between them.

In mathematical form, the equation looks like this.

G is the gravitational constant, measured at the following value.

Let's assign the values to our hypothetical question.

Stephy's mass: 40 kg

Earth's mass: 5,972,000,000,000,000,000,000,000 kg

Average elevation at Toa Payoh: 15 m

Distance from Earth's crust to core: 6,371,000 m

Height of Mount Everest: 8,848 m

r when Stephy is at Toa Payoh: 15 m + 6,371,000 m = 6,371,015 m

r when Stephy is on top of Mount Everest: 8,848 m + 6,371,000 m = 6,379,848 m

Plugging in the numbers...

There you have it - Stephy belongs to the strawweight category (going by MMA weight classes) whether she's at Toa Payoh or on Mount Everest. The gravitational force acting on Stephy does change with height above the Earth's surface, but as long as she's not flying off into outer space, the difference is so small it's not really significant...

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