Question

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

Answer 1

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.