Calculate the gravilational force of the Earth on the man 8 3 Calculate the gravilational force of the Earth Explain why the man and the child do not feel the gravitational attraction force between them as calculated in Question 8.1 Two metal balls with a mass of \( 8 \times 10^{4} \mathrm{~kg} \) and 2 \( \times 10^{3} \mathrm{~kg} \) respectively with their centres 340 cm apart. Calculate the gravitational force between them. 92 A hydrogen atom consists of a proton and an \( = \) electron The mass of the proton is about \( 10^{-27} \) kg and those of an electron \( 10-30 \mathrm{~kg} \) Calculate the gravitational force between them at a distance of \( 10^{-10} \mathrm{~m} \) \( \qquad \) \( \qquad \) \( \qquad \) The gravitational attraction force between two ships with a mass of \( 6 \times 10^{4} \mathrm{~kg} \) and \( 2 \times 10^{5} \mathrm{~kg} \) respectiveiy is 1,64 \( \times 10^{-2} \mathrm{~N} \). 10.1 Calculate how far the ships must be from each other. 10.2 If the distance between the ships is halved, how will this influence the force between them? 10.2 10.1 \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \)

To calculate the gravitational force between two objects, we can use the formula: \[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \] where: - \( F \) is the gravitational force between the two objects, - \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \)), - \( m_1 \) and \( m_2 \) are the masses of the two objects, - \( r \) is the distance between the centers of the two objects. Let's calculate the gravitational force between the two metal balls with masses \( 8 \times 10^{4} \, \text{kg} \) and \( 2 \times 10^{3} \, \text{kg} \) and their centers 340 cm apart. Given: - Mass of the first metal ball, \( m_1 = 8 \times 10^{4} \, \text{kg} \) - Mass of the second metal ball, \( m_2 = 2 \times 10^{3} \, \text{kg} \) - Distance between the centers of the two metal balls, \( r = 340 \, \text{cm} = 3.4 \, \text{m} \) Now, let's calculate the gravitational force between the two metal balls. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(6.674\times 10-11\right)\times 8\times 10^{4}\times 2\times 10^{3}}{3.4^{2}}\) - step1: Multiply the numbers: \(\frac{\left(66.74-11\right)\times 8\times 10^{4}\times 2\times 10^{3}}{3.4^{2}}\) - step2: Subtract the numbers: \(\frac{55.74\times 8\times 10^{4}\times 2\times 10^{3}}{3.4^{2}}\) - step3: Convert the expressions: \(\frac{55.74\times 8\times 10^{4}\times 2\times 10^{3}}{\left(\frac{17}{5}\right)^{2}}\) - step4: Multiply: \(\frac{8918400000}{\left(\frac{17}{5}\right)^{2}}\) - step5: Simplify the expression: \(\frac{8918400000}{\frac{17^{2}}{5^{2}}}\) - step6: Rewrite the expression: \(\frac{222960000000}{17^{2}}\) - step7: Evaluate the power: \(\frac{222960000000}{289}\) The gravitational force between the two metal balls is approximately \( 7.71 \times 10^{8} \, \text{N} \).