f = ma. that means if i am pushing a box at a constant speed, there is no force. how can this be?

Question

if speed is constant then a = 0, leading to no foce being involved. how can this be, if i am constantly applying force to the box to push it?

Answer 1

F=ma is true, there is not *net* force on the box. The force you apply is there to exactly balance the force of friction.

Answer 2

All the answers thus far are correct.

The f in f = ma is "net" force. That is it's whats left over (the net) after all forces acting on m have been summed up vectorally. If the sum of all forces is zero, then f = 0 = ma; so, since m (the mass of the box) is always some positive value, a = 0. If the sum of all forces is not zero, then f <> 0 and ma <> 0; so a <> 0 and the body, e.g., your box, will accelerate or decelerate. Deceleration is just negative acceleration.

The point is, the velocity of the box will not change without a net force acting on it. That is, if the box was moving when f = 0, it will stay moving until f <> 0 so that a <> 0 and it either slows down (if a < 0) or speeds up (a > 0).

In physics problems we are frequently asked to calculate terminal velocity of a free falling body through the air. To do this, we start with f = ma; where m is the body and f is the net vertical forces (up and down). Thus we have f = ma = W - D(v); where W is the weight of the body (force of gravity) and D(v) is the drag force from air friction. The v in D(v) means drag force is a function of velocity of the falling body.

From f = ma = W - D(v), we can see as the velocity of the body increases, due to the a in ma, the net difference between W, which is fixed, and D(v), which is increasing, gets smaller and smaller. Finally, at some velocity, W = D(v), the drag force equals the weight of the body. When that happens v = V, the terminal velocity; so called because v will go no faster, it has ended acceleration...f = ma = W - D(V) = 0 and, therefore, a = 0 when W = D(V).

Notice that W > 0 and D(V) > 0; so, even though f = 0 at terminal velocity V, there are still forces acting on the falling body. Same way with your box. In its case you might have f = P - F = ma = 0; where P is the push and F is the force of friction opposing the push. So when your push exactly equals the force of friction, but in the opposite direction, a will be zero. The box will continue to move at whatever speed is was when a became zero.

All these concepts, f = ma, equal but opposite forces, and a body not changing velocity unless acted on by a net force, are embodied in Newton's three laws of motion. Suggest you check out the cited source if you are interested.

Answer 3

Sure F = ma but this applies in an ideal situation where the only force exerted on the object is by the hand/machine/whatever. The F really represents Fnet, the total effective force on the object. The force in real life needed to push something at a constant speed must overcome frictional force, which is moving in the opposite direction of motion. If the force exerted by your hand and by friction is the same, F net would be 0 and ONLY THEN would the box move at a constant speed

Answer 4

Your acceleration is necessary to overcome gravity, friction, etc. If you pushed the box in open space, where there was no gravity, etc to fight against, there would be no Force necessary to keep the speed constant. But, since you have to fight friction and gravity, if you were NOT pushing, the acceleration would be negative, and the box would SLOW down. You are applying the POSITIVE force necessary to overcome those NEGATIVE forces, just to keep the acceleration constant.

Hope that helps!

Answer 5

Once you got it to a certain speed it would keep on going with no force in theory, however because there is friction off the floor that is pushing in the opposite direction so you are constantly having to push.

Answer 6

You take the current speed and find out how far it is from 0. You are not going at that speed forever, so it is a constant acceleration.

Answer 7

Interesting. My house weighs about 80,000 kg if I lean on the back wall to sunbathe I apply a force of about 200 Newtons this means that my house should be accelerating at 1/400 Meters per second , after 1/2 hour sunbathing my house should be moving away at 3.5 meters per second but it doesn't! How can this possibly be?

Answer 8

Acceleration is a time derivative with respect to velocity.

a = dv/dt.

Speed is simply the magnitude of the velocity; if it is zero, then dv/dt = 0, which makes f = 0. Note that dv over some given interval is v2 - v1. In this case, v2 = v1, because the velocity is not changing over the interval.

Hope this helps.

Answer 9

it is sigma f = ma
where sigma means the sum of the forces
So when you are moving at a constant speed, the forces are balances and hence there sum of the forces is 0