The weight of a standard object defined as having a mass of exactly 2.9 kg is measured to be 28.449 n. in the same laboratory, a second object weights 48.7 n. what is the mass of the second object? answer in units of kg

Mass of the object m = 2.9 kg 
Force F1 = 28.449 N 
F1 = m1 x a => a = F / m => 28.449 / 2.9 => a = 9.81, which is gravitational acceleration. 
In the same lab, a = g = 9.81, second object F2 = 48.7N = m2 x a 
m2 = F2 / a => 48.7 / 9.81 => m2 = 4.96 kg 
Mass of the second object m2 = 4.96 kg

If the units is expressed in terms of Newtons, that's a unit of force. The relationship between force and mass is Newton's Second Law of Motion.

F = ma

In this case, a is the acceleration due to gravity. Let's solve a first.

28.449 N = (2.9 kg)(a)
a = 9.81 m/s²

We use this to find the m of the second case.
F = ma
48.7 N = m(9.81 m/s²)
m = 4.96 kg