Hello. I am in a middle school science course and do not understand a certain part of the curriculum.
I understand that one can convert an amount of kilograms (a unit of mass) to Newtons (a derived unit of force). But why are we able to convert from one unit to another?
Also, in a problem where the acceleration is '2m/sec/sec' and the mass is 40 kg, say I want to find the force. I plug those in to the equation 'A=F/M'. I multiplied both sides by the mass (40 kg) to get the force. Now I'm left with Force= 2m/sec/sec times 40 kg. What should I do from there? The answer is apparently 80/N but I need help getting there.

Thanks.

I understand that one can convert an amount of kilograms (a unit of mass) to Newtons (a derived unit of force). But why are we able to convert from one unit to another?

Good question, and it's an area that often cause confusion. "Kg" is a unit of mass, and so is fundamentally different from a force. They can not be "converted " one to other. But one very common use of force in every day life is to talk about how much something weighs. Weight is force due to gravity, and is found by multiplying an object's mass by a constant for the "acceleration due to gravity," which for gravity on earth is written as the letter 'g' and is equal to about 9.8m/s^2. So for example an object of mass 100Kg on earth weighs 100 Kg x 9.8m/s^2 = 980 Kg-m/s^2 = 980 N. In discussing how much something weighs we should use units of newtons, not Kg, and when people say something "weighs" 100 Kg they are wrong - its mass is 100 Kg and its weight(on earth) is 980N. Yet common usage is to determine an object's mass using a scale that converts the force of gravity to the equivalent mass that creates that force due to gravity on earth. I hope this is not too confusing and explanation.



Also, in a problem where the acceleration is '2m/sec/sec' and the mass is 40 kg, say I want to find the force. I plug those in to the equation 'A=F/M'. I multiplied both sides by the mass (40 kg) to get the force. Now I'm left with Force= 2m/sec/sec times 40 kg. What should I do from there? The answer is apparently 80/N but I need help getting there.

Thanks.

The thing to remember is that the newton is a unit of force where 1 N = 1 Kg-m/s^2. So using your example: 80 Kg-m/s^2 = 80 N. This is the force needed to accelerate the 40 Kg mass at 2 m/s^2.

F=m.a
m\to kg
a\to \frac {m}{s^2}
F\to N(Newton=kg.\frac {m}{s^2}
F_N=20_kg.2_{\frac {m}{s^2}}
F=40 N