Universal Gravity Problem Set
Follow the Problem Set Instructions & Rubric to complete and submit the following questions:
1. What is the magnitude of the force of gravitational attraction between two \( 1.8 \times10^8kg \) spherical oil tanks with their centres \( 94m \) apart? [Answer: \( 2.4 \times10^2 N \)]
2. A \( 50.0kg \) student stands \( 6.38 \times 10^6 m\) from Earth's centre. The mass of Earth is \( 5.98 \times 10^{24} kg \). What is the magnitude of the force of gravity on the student? [Answer: \( 4.90 \times10^2 N\)]
3. Jupiter has a mass of \( 1.90 \times 10^{27} kg\) and a radius of \( 715 \times 10^7 m\). Calculate the magnitude of the acceleration due to gravity on Jupiter. [Answer: \( 24.8 m/s^2\)]
4. A space vehicle, of mass \( 555 kg \), experiences a gravitational pull from Earth of \( 255 N \). The mass of Earth is \( 5.98 \times 10^24 kg\). How far is the vehicle (a) from the centre of Earth and (b) above the surface of Earth? [Answer: a) \(2.95 \times 10^7 m \), b) \( 2.31 \times 10^7 m \)]
5. Four masses are located on a plane as in the figure below. What is the magnitude of the net gravitational force on \( m_1 \) due to the other three masses? [Answer: \( 6.1 \times 10^{-10} N \) [right \( 45^o \) down]]
6. The mass of Earth can be calculated by applying the fact that an object's weight is equal to the force of gravity between Earth and the object. The radius of Earth is \( 6.38 \times 10^6 m \).
a) Determine the mass of Earth. [Answer: \( 5.99 \times 10^{24} kg \)]
b) At what stage is the historical development of science would physicists first have been able to calculate the Earth's mass accurately? Explain your answer.
c) What effect on society is evident now that we accurately know Earth's mass?