Would it be possible for an object travelling along a perfectly straight path to change (opposite) directions without reaching a speed of 0.
Kind of like a baseball being hit by a bat. Can it remain perfectly still for a moment?
In actual media, acceleration isn’t instantaneous, and, more importantly, isn’t transmitted to the entire medium simultaneously. So in the baseball/bat situation, you would have a wave of compression that transmitted force from one end of the baseball to the other. At some point, the average speed of the particles in the baseball would be pretty close to zero, but some would still be going forward, not having got the force of the bat yet, while others would be traveling in the bat’s direction pushing the opposite way of the rest of the ball.
Instantaneous change of velocity would be infinite acceleration, which by f = ma would require infinite force. So Isaac Newton says “no”.
I’m no phycisist but I’d think it would be impossible for it not to. For anything to reverese its direction it would have to completely halt its forward motion before moving backwards. Now, if there was any deviation from that line in any direction then the object would still remain in lateral motion even as forward motion halts to reverse direction (assuming a lack of fruction or other opposing force to halt said lateral motion)
I am not a Physicist, but firstly, your two questions seem to be asking opposite things. So, secondly, the answers seem to be (intuitively): no and yes.
That’s really what I was trying to avoid, the whole compression thing. I’m really talking about maybe a steel ball willed by some force to go from 1mph to -1mph, or 1000mph to -1000mph (by negative I mean opposite direction).
That’s what I was thinking
Yes. If you look at the motion as a curve, there is a point where the tangent = 0. So an idealized ball will come to a complete halt before reversing direction.
OK, to make this a little easier lets postulate a ball of uniform material in a changing but, at any given instant, uniform gravitational field. That way we can apply a force evenly over the entire object and not have to worry about pressure waves in the ball unless we start to get to relativistic speeds.
Force fields impart acceleration, acceleration and time gives motion, and motion and time gives displacement. You cannot have an infinite force, therefore you cannot have an infinite accerlation. So, your very large but finite force imparts a very large but finite acceleration to the object opposite its direction of motion. As the acceleration is finite, velocity (the time intergral of acceleration) will be continuous.
The intermediate value theorem states that for a continous function F with two points, A and B, if F(A) is positive and F(B) is negative there exists a point C in between A and B for which F©=0. Simply stated, if you have a continuouse line above zero at one point and below zero at another, it will have to cross zero at some point to connect them.
This all goes to pot if you have an infinite force. We at NASA would be very interested in hearing from you if you manage to come up with this.
So, here’s my related question:
An iron locamotive engine traveling down the tracks at a constant speed of 60mph. It’s cast iron so nothing will dent it or mush into it’s surface.
Floating in mid air (similar to a fly) along the tracks is an iron ball bearing. Unmoving at zero velocity. A solid bearing that will not compress or distort.
Now it is common law that an object at rest can not obtain an instant velocity but must accelerate to it (even if it is very quickly and over an incredibly short distance). So, if that ball bearing gets hit (and sticks) to the front of the train it needs to accelerate from 0 to 1 to 2 to 3mph… up to 60 mph. At some point the bearing will have to be going 30 mph.
Now, if the bearing is at zero, and begins accelerating at the moment it makes impact with the train, when is it at 30mph? And does this mean the train is also at 30mph? I don’t think so. So how can the bearing be touching the constant velocity train (almost making them instantly one) and be going 30mph at an instant in time while the train is going 60mph?
HardWorker and Hampshire offer situations built around a metal ball of iron or steel. They seem to assume that a hard metal ball will be inelastic, in contrast to a baseball or tennis ball.
Now here’s the boing, and I’m not so sure I believe it myself. A high school teacher once assured me that, if you dropped a steel ball and a rubber ball of equal weight on a heavy steel plate, the steel ball would bounce higher. He said that showed the steel to be more elastic.
I’m not much of a fizzy cyst, and I probably will never be. Was this teacher correct? Was he talking out of his terminal digestive port?
Steel balls bounce very high. So do golf balls. Most rubber balls hardly bounce at all comparatively.
From Google Answers
Or read this page from How Things Work on all sorts of bouncing questions.
Ah, but he said “speed” not velocity. The distinction is that velocity is directional–in this case we’d be talking about velocity along the line of movement–and speed is nonoriented. So it is entirely possible for an object–say, a racecar going around a track–to have a high average speed (200km/hr), but a zero average velocity. We’re talking about instantaneous speeds and velocities here, of course, but the principle remains; a moving object can’t ever reverse direction without the velocity (in that direction) being zero at some point, but it can maintain a speed (in orthogonal directions) while that occurs.
Amazingly enough, your high school teacer was correct; the steel ball will bounce higher than than rubber. The same with ceramic, provided of course that it doesn’t fracture. This seems counterintuitive because normally when we drop something very heavy–say, a bowling ball–it tends to deform if not destroy the surface on which it falls. This is because the contact area is very small (mathematically it’s a point, although both the ball and surface will deflect a little bit) creating what are called Hertzian stresses, a highly concentrated stress differential focused about the contact point. Because a sphere shape is geometrically strong, unless the modulus of elasticity is very low (as in the rubber ball) the surface material usually gives way, absorbing energy as it does. The reason a rubber ball bounces as highly as it does is that it is willing to give way (within its elastic range) before the contact surface does, and so retains most of its energy. If, however, you bounced a steel ball bearing and a small rubber ball against a totally inelastic surface, the ball bearing would bounce higher every time.
Stranger
Unfortunately you can’t avoid “the whole compression thing.” All of the equations in the elementary physics books are for point masses. Actual objects are composed of many, incremental “point masses” and when other objects apply forces on them the forces are not applied to all of the increments in the objects at the same time.
All of the increments of the ball do pass through zero velocity in the direction of their travel by they do so at different times and over a small period of time, and that also goes for a steel ball. Think of the ball and bat as both being made of tiny, solid cubes, slightly separate from each other and interconnected by springs. Ball and bat are both elastic. The cubes in the ball that are in contact with the bat will slow and reverse direction over a small increment of time so the ball will deform. This will exert forces on the other cubes in the ball which, over time, will also slow, come to a stop and reverse direction.
Unfortunately you can’t avoid “the whole compression thing.” All of the equations in the elementary physics books are for point masses. Actual objects are composed of many, incremental “point masses” and when other objects apply forces on them the forces are not applied to all of the increments in the objects at the same time. As Ludovic said, this results in a compression wave that travels through the ball.
All of the increments of the ball do pass through zero velocity in the direction of their travel by they do so at different times and over a small period of time, and that also goes for a steel ball. Think of the ball and bat as both being made of tiny, solid cubes, slightly separate from each other and interconnected by springs. Ball and bat are both elastic. The cubes in the ball that are in contact with the bat will slow and reverse direction over a small increment of time so the ball will deform. This deforming will take the forms of a flattening of the ball and bat. The flattening results in a change of direction from straight forward to a more complex motion that results in the forward motion, but not necessarily all motion as Stranger noted, of the cubes to become zero.
English is my native tongue, honest, but you can’t tell from the above. Make that last bit read …"results in the forward motion, but not necessarily all motion as Stranger noted, of the cubes becoming zero.
Pish and tosh. You know very well that unless you answer what a person means rather than says no science question would ever get answered on the Internet.