Can a force of 3 newtons move a 1-kg mass 3 meters and a 3-kg mass one meter?

Answer 1

I think you're confusing force and work. Both are related, but they're not the same thing. Let's review a few things, first. If an object of mass, m, experiences an acceleration, a, then we know the sum of the forces acting on the object is m * a. In other words, F = ma. The unit of force is the newton (N). Note that distance (or displacement) does not factor in the equation. If an object experiences a force, F, and moves a distance, d, in the direction of the force, we know that the work done on the object is F * d. In other words, W =Fd. The unit of work is the newton-meter, which is known as a joule. Note that mass does not factor in the equation. So where the heck does this leave us? The answer to your question is yes to both parts. If the mass -- even a large one -- is resting on a frictionless surface, even the smallest force applied to it will cause it to accelerate in the direction of the force. For the numbers you provided, it will take no time for the 3-newton force to move either the 1-kg mass three meters or the 3-kg mass one meter. Let's keep exploring to see whether we can learn anything else from this problem. Since F = ma, we may write a = F/m, so the 1-kg mass accelerates at 3N/1kg = 3 meters per second squared. (Note this assumes a frictionless environment.) For the 3-kg mass, we have

a = 3N/3kg = 1 meter per second squared (m/s2). So, the larger mass doesn't accelerate as rapidly. How about the work done? In both cases, the force acting on the objects is 3 newtons. The work done to move the larger mass one meter is 3N * 1m = 3 joules. The work done to move the smaller mass is 3N * 3m = 9 joules. Keep in mind that in the presence of friction -- between the object and the surface it rests on, for example -- a 3-N force may not be enough to overcome the frictional forces working against it, especially for large masses or for surfaces with very high friction coefficients.

Answer 2

No. It takes 1 newton to accelerate a 1 kg mass at 1 meter per second per second. Some points to understand or just accept. Newton is a measure of force. Sir Isaac newton taught us that Force = mass times acceleration. meter per second refers to velocity. In simple physics, we ignore all sources of resistance, so it takes no force to maintain a velocity of 1 meter per second. It does take a force to change the velocity of an object. This is acceleration and is measured in meters per second per second. This unit is also called meters per second squared. Either name refers to the same unit. It tells us how fast something is changing velocity. At a constant acceleration of 1 meter per second per second, the velocity is increasing by 1 meter per second each and every second. At a constant acceleration of 9.8 meters per second per second, the velocity is increasing by 9.8 meters per second each and every second. The amount of force is takes in a frictionless environment (like outer space) to accelerate a 1 kg mass at a rate of 1 meter per second each and every second is defined as 1 newton. In our real world, it is tough to escape resistance (things like air resistance and friction between to surfaces). So force is often needed to overcome resistance and maintain a steady velocity. 1 newton is roughly the force needed to pull a 1/2inch thick spiral notebook slowly across a smooth wood table top.