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2 years ago

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Eee A student conducts an investigation to determine how the force of gravity affects different objects dropped from different h

eights. The student tests each object one time and announces that all objects experienced gravity the same way. What is wrong with the student's reasoning?

1 answer:

ss7ja [257]2 years ago

3 0

Answer:

For which the reasoning of the boy is correct for small heights, but as height increases his analysis is not correct.

Explanation:

The force of gravity comes from Newton's second law with the force the universal attraction

F = ma

F = $G \frac{m_1 M}{(R_e +h)^2}$

we substitute

$G \frac{m_1 M}{ (R_e+ h)^2}$ = m₁ a

where Re is the radius of the Earth 6.37 106 m

a = $G\frac{M}{R_e^2} \ ( 1 + \frac{h}{R_e})^{-2}$

In general, the height is much less than the radius of the earth, therefore the term ha / Re is very small and we can use a series expansion leaving only the first fears.

(1 + x)⁻² = 1 -2x + $\frac{2 \ 1}{2!}$ x²

we substitute

a = g₀ ( $1 - 2 \frac{h}{R_e}$ )

with

g₀ = $G \frac{M}{R_e^2}$

let's launch the expression.

* For small height compared to the radius of the earth we can neglect the last term

g = g₀

* For height comparable to the radius of the Earth

g = g₀ $(1 - \frac{2h}{Re} )$

We see that the acceleration of gravity is decreasing.

For which the reasoning of the boy is correct for small heights, but as height increases his analysis is not correct.

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