Answer to Question #287292 in Physics for Hana

Question

Data required: G = 6.67 x 10-¹¹ N m² kg-²

mass of the Earth = 6.0 x 10^24 kg radius of the Earth = 6.4 x 10^6 m gravitational field strength close to the surface of the Earth is 9.8 N kg-1 15

1.) What is the gravitational potential energy of a 60 kg student on the surface of the Earth? What then, is the minimum energy that would be required to get this student completely out of the Earth’s gravitational field?

2.) You’re in the design of mission carrying humans to the surface of the planet Mars, which has a radius of 3.38 x 106 m and a mass of 6.24 x 1023 kg. The Earth weigh of the Mar’s lander is 39,200 N. Calculate its weight and the acceleration due to Mar’s gravity at 6.0 x 106 m above the surface of Mars.

(Show the solution if it's possible, thanks)

Answer 1

1) The energy is

$$U=GMm/R=3.75·10^9\text{ J}.$$

This is the energy required to get this student completely out of the Earth’s gravitational field.

2) The acceleration due to gravity on Mars is

$$g_M=\dfrac {GM}{R^2}=3.64\text{ m/s}^2.$$

The weight is

$$W=g_Mm=g_M\dfrac{W_E}{g_E}=14560\text{ N}.$$