So if force =mass * acceleration, then an object moving at a constant velocity has zero acceleration, and thus force = zero.
So is f=ma actually mean net force or some other definition?
And I’ve been told work is force * distance, so sn object moving at a constant velocity would also have zero work? Which doesn’t sound correct so I’m confused on what exactly work defines
In: 5
In:
> **F** = m **a**
The “F” is the resultant force, or the net force, or the vector sum of all forces.
Work done on an object as a result of a specific force is the force * distance (or if we’re being more precise, the path integral of **F.ds**).
So these are different forces. The first is the net force, the second is a specific force.
Quoting Wikipedia, “work is the energy transferred to or from an object via the application of force along a displacement.”
So as you note, if an object is moving at constant velocity, there must be no net force acting on it – i.e. all forces must cancel each other out. So there is no overall work done on or by the object. This is the **work-energy principle**:
> the work done by all forces acting on a particle (the work of the resultant force) equals the change in the kinetic energy of the particle
Here we have no change in kinetic energy, so we have no net work done.
Where things get a bit complicated is that work doesn’t just transfer energy to an object from an object, it can also shift energy from one form to another form.
————-
If we take the example of lifting an object up a certain height *h* at constant velocity, there will be two forces acting on it. Some force that is lifting it up, *L*, and its weight pulling it down *W*. The work done on the object by the lifting force will be:
> w.d. = L * h
The work done by the weight will be:
> w.d. = W * h
(noting that W will be negative if we are taking up to be the positive direction). Then by F = ma, if it is at constant velocity we know *a* = 0, and so:
> F = L + W = ma = 0
> L = -W
and so we get that the work done on the object by the lifting force is equal and opposite to the work done by the weight; so there is no overall change in work on the object.
But the object *has gained energy* – it has gained gravitational potential energy. While the work done by the lifting force is transferring energy from whatever is lifting it to the object, the work done by the weight is shifting that energy into the form of gravitational potential energy (or alternatively, transferring that energy into the object-Earth system/gravitational field).
Potential energy is a bit of a fudge, in some ways. The maths works, but it can take a bit of thinking to get your head around it.
Latest Answers