The standard acceleration (at sea level and 45◦ latitude) due to gravity is 9.806 65 m/s2. What is the force needed to hold a mass of 2 kg at rest in this gravitational field? How much mass can a force of 1 N support?

a) Remember Newton's second Law:

F = m*a

This means that the forces that is being exerted over an object is equal to the mass of the object times the acceleration that it has.

In this case, in order to hold the mass you need a force with the same magnitude but opposite direction to the gravitational force. The magnitude of this force would be the mass of the object times the gravitactional acceleration:

F = 2kg*9.80665m/s² = 19.6133 N

b) Using again Newton's second Law, we can issolate mass from that equation:

m = F/a

Then, the mass that a force of 1N can support is equal to:

m = 1N/9.80665m/s² = 0.102 kg