force needed to curve a moving object?

Question

lets say object A is moving in a straight line, and you throw another object (B) towards it from a 90 degree angle. how much force is needed to "curve" the path of the object A 45 degrees from the straight line? i realize that F=mass*velocity, but i assume i need some trig function to correct the path of object A?

Answer 1

If you mean that these objects will collide, you must use conservation of momentum. Momentum = mass*velocity. So to make it change direction by 45 deg, the magnitude of momentum of object B must be equal to the magnitude of momentum of object A.

Answer 2

What's left out are masses and final velocities, making this problem an indeterminate one. But let's assume that A has a velocity of v in the x direction, and after the collion it has a velocity of v in the y direction as well, so that it's now travelling at 45 degrees from the original track. The force equaiton is actually:

F = ma

where a is acceleration, not velocity. Now, we want to accelerate the original mass m to velocity v in the y direction, and so force is applied, and we know that:

a = F / m

If this force is applied for a period of time, say dt, where d is delta, or change in time, we have:

a dt = F dt / m = v
F = mv / dt

Now, mv is just the y component of the momentum of the original mass, and the force needed to deflect it to a trajectory of 45 degrees is found by dividing the desired final y component of the momentum of the original mass by the time in which this force is exerted. In other words, if another object struck the original mass, and if they are both very hard so that the impact lasted a very short time, the force would be very high. However, if one or both objects was soft and elastic so that the impact lasted longer, the force would be smaller. This explanation also holds true for impact between charged particles where there is no actual contact, the collision being mediated by a force, but the mathematics is more complicated because such force fields are defined by a function, and the force involved in the "impact" would actually vary over time.

Answer 3

Momentum = mass * velocity
Momentum must be conserved.
More on momentem at Wikipedia:
http://en.wikipedia.org/wiki/Momentum

Simplify the problem by thinking of pool balls on a frictionless table.

Hope this helps!

Answer 4

In Newtonian mechanics, the respond is "no": any deviation from "right this moment course with a uniform velocity" incorporates an *acceleration*, and in accordance to Newton, accelerations advise a internet stress imbalance. yet that is not particularly authentic, needless to say. there is not any internet stress on the solar, yet you may easily say that, out of your perspective in the international, it follows a curved course. this is a typical supplies of *non-inertial reference frames* :: in case you're measuring each thing with appreciate to an accelerating coordinate device, then a lot of alternative issues seem to develop up without internet forces. the elementary thank you to come back a suitable description is often to invent "fictitious forces" that create those accelerations. as an occasion, in case you %. up a bucket finished of water and spin it around in a circle, the water maintains to be in the bucket in case you swing it quickly sufficient: in the reference physique of the bucket, there's a fictitious centrifugal stress that factors in the direction of the backside of the bucket, protecting the water interior. whether, i've got in simple terms spoken right here approximately *Newton*. And Newtonian mechanics grow to be superceded in the midst of the final century via countless substantial different theories. standard relativity, especially, fashions the full "stress of gravity" as a fictitious stress: relativity incredibly defines a hyperbolic geometry the place issues *do not* certainly shop shifting uniformly in a right this moment line while there is not any stress on them: incredibly, they certainly persist with curved paths while they bypass close to heavy gadgets like planets and stars. From a typical relativity perspective, all of those satellites in orbit around the Earth are easily following around orbits: yet there is not any stress on them; they are in simple terms in the midst of a various, non-Euclidean geometry. (This has some bizzarre outcomes that we've experimentally demonstrated: as an occasion, that clocks could pass slower closer to the Earth than they do in area; and that gentle -- that's massless -- should additionally be tormented by gravity and be bent around stars.)