An astronaut’s pack weighs 17.5 N when she is on the earth but only 3.24 N when she is at the surface of a moon. (a) What is the acceleration due to gravity on this moon? (b) What is the mass of the pack on this moon?
Solution 20E The weight is defined as how much normal reaction an object gets. An object of mass “m” is placed on the horizontal surface of earth exerts a force f mg on earth’s surface. By the same time, according to Newton’s 3rd law, it gets the same normal reaction force mg from earth’s surface. 2 So the weight will be mg = mass × 9.8 m/s . Step 1: The astronaut’s weight on earth is, w = mg = 17.5 N m = 17.5 N / 9.8 = 1.785 kg The mass of the astronaut is 1.785 kg. a) On the surface of moon she weighs 3.24 N. mg moon = 3.24 g moon = 3.24 / 1.785 = 1.815 m/s . 2 The acceleration due t gravity at moon is 1.815 m/s . b) The mass is an invariant quantity which is same on earth as well as moon or anywhere else. So, the mass on the moon is 1.785 kg.