weight force mass?

Question

An object is on a scale, and a force of 200 Newtons is being pushed on it from above. The scale reads 75.0 lbs. What is the mass of the box (in kg)?

Now, I know the force is 200 N, g = 9.8 m/s^2. I need the mass. F = m*g. How do I incorporate the weight into this equation?

Answer 1

1 lbs = 453.6g = 0.454kg
So the reading on the scale = 0.454 x 75 = 34.05kg

Using F = m x g the weight of the object and the force pushing down on it = 34.05 x 9.8 = 333.7N

So now we subtract the 200N push force to find the box's true weight: 333.7 - 200 = 133.7N

Hence we use the F = ma rrearranged to find the mass in kg:

F = ma
m = F/a
m = 133.7 / 9.8 = 13.7kg

Answer 2

Did you notice the scale is in pounds, while the push is in Newtons (kg-m/sec^2). You need to change one or the other; so that your force units are in the same units. Since you are looking for mass in kg, I'd suggest you change the 75 pounds into Newtons.

That being done, the S = 75 lbs converted to Newtons = W + P; where W is the weight of the mass and P is the push = 200 N. Thus W = mg = S - P; so that m = (S - P)/g and once you have S in Newtons, you have all the numbers to solve for m, the mass of the box.