Question

Numner 5 part a and b and c and d

Answer 1

5)

a)

In order to calculate the force acting on the masses, we can use the formula below:

`F=(G\cdot M\cdot m)/(d^2)`

Where G is the gravitational constant (G = 6.674 * 10^-11), M is the greater mass, m is the smaller mass and d is the distance between the masses.

So, for M = 6 * 10^24 kg, m = 1 kg and d = 6.4 * 10^6 m, we have:

`\begin{gathered} F=(6.674\cdot10^(-11)\cdot6\cdot10^(24)\cdot1)/((6.4\cdot10^6)^2) \\ F=(40.044\cdot10^(13))/(40.96\cdot10^(12)) \\ F=9.78\text{ N} \end{gathered}`

b)

The force calculated in item a) will act on both masses, therefore the force acting on the larger object is also F = 9.78 N.

c)

The acceleration can be calculated using the second law of Newton:

`\begin{gathered} F=m\cdot a \\ 9.78=1\cdot a \\ a=9.78\text{ m/s2} \end{gathered}`

d)

Using the second law of Newton again, we have:

`\begin{gathered} F=M\cdot a \\ 9.78=6\cdot10^(24)\cdot a \\ a=1.63\cdot10^(-24)\text{ m/s2} \end{gathered}`