Question for the Science Guys (Jewett, Dr. Dave)

[Jen_Cen]

If I shoot a ball in a straight line, and the table is NOT perfectly level, causing the ball to miss the target by, say 1.0 inch...

Shouldn't all speeds cause the ball to miss by the same 1.0 inch? I don't see why a slower shot will result in missing more severely.

I would think that gravity and geometry would decide the outcome, not the amount of time the ball is in motion.

 

[dave sutton]

no the slower a ball rolls the more it will roll off.
think about how a breaking putt works in golf. the harder you putt the ball the straighter it goes but you cant properly sink the putt bc the speed is too great to drop into the cup. so... the players over play the break for proper speed. im sure ve;ocity factors in the equation if your writing out the problem on paper

same with pool

 

[sde]

If I shoot a ball in a straight line, and the table is NOT perfectly level, causing the ball to miss the target by, say 1.0 inch...

Shouldn't all speeds cause the ball to miss by the same 1.0 inch? I don't see why a slower shot will result in missing more severely.

I would think that gravity and geometry would decide the outcome, not the amount of time the ball is in motion.

Think of it as trying to swim across a river. The slower you swim the farther downstream you will be when you reach the other side.

Steve

 

[Jen_Cen]

Think of it as trying to swim across a river. The slower you swim the farther downstream you will be when you reach the other side.

Steve

Great explanation...reminds me of physics class way back when...and adding up x and y vectors...ack.

 

[Balabushka]

Think of it as Golfer that's trying to swim across a river chasing after a cue ball.

 

[Bob Jewett]

If I shoot a ball in a straight line, and the table is NOT perfectly level, causing the ball to miss the target by, say 1.0 inch...

Shouldn't all speeds cause the ball to miss by the same 1.0 inch? I don't see why a slower shot will result in missing more severely.

I would think that gravity and geometry would decide the outcome, not the amount of time the ball is in motion.

The curved path of the ball on a tilted table is close to a parabola if it doesn't slow down significantly during the shot. That's not always a good assumption, but for the purposes of explanation it is close enough.

The deviation of a ball due to a non-flat table is more or less the same as a ball being deflected by gravity when thrown horizontally. The faster the ball is thrown, the less it will drop before it gets to its target. The reason is that gravity (or the tilt of the table) takes time to act on the object and the longer you give the force of gravity (or the force due to the tilt of the table), the more the ball will deviate from its original direction.

If a ball rolls off by an inch for a fairly slow shot, it will only be off 1/4 of an inch if you shoot at twice the speed. If you take the slowing of the ball during the shot into account, I think the ratio of errors will be even larger.

The worst case for roll-off is when the table tilts at a right angle to the path of the ball. If the table tilts with or against the path of the ball, the ball will go straight, but might be a little slow or fast.

 

[Tom M]

( I see that Bob beat me to it with a much more complete answer)

The other explanations are essentially correct. The scientific explanation has to do with time. Assuming the exact same shot line, the force of gravity is the same along that line and is independent of the speed of the shot. What's different is that for the fast shot, gravity is in effect for a shorter time, resulting in less deflection than a slower shot.

Now, just for fun, to see if you understood Bob's post, here's the test question:

If you fire a bullet on a perfectly level trajectory, it will eventually land on the ground (provided it doesn't hit anything first). If you drop a bullet at exactly the same time from the same height as the gun, which bullet will hit the ground first?

Tom

 

[Bob Jewett]

Think of it as trying to swim across a river. The slower you swim the farther downstream you will be when you reach the other side.

Steve

While the sense of the difference is correct for this illustration, the relative quantity of "deflection" at different speeds comes out wrong. When swimming across a river, the "deflection" is directly proportional to how long it takes you to cross. In the case of a ball being deflected by gravity or a tilted table, the deflection is proportional to the square of the time taken. If you take twice as long, you will miss by four times as much.

 

[Jen_Cen]

( I see that Bob beat me to it with a much more complete answer)

The other explanations are essentially correct. The scientific explanation has to do with time. Assuming the exact same shot line, the force of gravity is the same along that line and is independent of the speed of the shot. What's different is that for the fast shot, gravity is in effect for a shorter time, resulting in less deflection than a slower shot.

Now, just for fun, to see if you understood Bob's post, here's the test question:

If you fire a bullet on a perfectly level trajectory, it will eventually land on the ground (provided it doesn't hit anything first). If you drop a bullet at exactly the same time from the same height as the gun, which bullet will hit the ground first?

Tom

They will both land at the same time, theoretically.

Although in reality there's probably aerodynamic effects to consider.

 

[sde]

While the sense of the difference is correct for this illustration, the relative quantity of "deflection" at different speeds comes out wrong. When swimming across a river, the "deflection" is directly proportional to how long it takes you to cross. In the case of a ball being deflected by gravity or a tilted table, the deflection is proportional to the square of the time taken. If you take twice as long, you will miss by four times as much.

Is what you're saying because of the acceleration due to gravity vs the constant speed of the river?

Steve

 

[SedateMe]

If you fire a bullet on a perfectly level trajectory, it will eventually land on the ground (provided it doesn't hit anything first). If you drop a bullet at exactly the same time from the same height as the gun, which bullet will hit the ground first?

Tom

They hit the ground at the same time. I remember that from the 6th grade.

 

[Bob Jewett]

Is what you're saying because of the acceleration due to gravity vs the constant speed of the river?

Steve

Yes. The table (actually, gravity) accelerates the ball in the direction of the tilt. The most extreme example is when a ball is rolling along the "low" end of the table and the ball keeps bouncing off the same cushion. I used to play on a table where one side was so low you could roll a ball bouncing along the side cushion and if you timed it right it would land in the side pocket.

 

[jay helfert]

Bottom line, if a ball rolls off by one inch, you better get your table re-leveled. That's a bad roll off you have there.

 

[Andrew Manning]

They will both land at the same time, theoretically.

Although in reality there's probably aerodynamic effects to consider.

Since you seem to have already gotten the answer you needed, I figure there's no harm in following this tangent.

If there's any aerodynamic lift acting on the bullet (due to spin or bullet shape or whatever), the "same time" notion is out the window. Also, due to the high muzzle velocity, if the gun is aimed above or below horizontal by even a tiny fraction of a degree, that will result in a significant vertical component to the initial velocity, which the dropped bullet doesn't have.

Also, the "same time" answer assumes a flat and infinitely large earth. In actuality, there exists a speed where if you shoot a bullet level to the ground, it will increase in height rather than decrease. This occurs when the earth's curvature means the ground retreats from the path of the bullet faster than gravity accelerates the bullet towards the ground. The speed where the curvature is just keeping up with the acceleration due to gravity, such that the free-falling object stays at the same height relative to the ground, is known as orbit velocity.

-Andrew

 

[hemicudas]

Bottom line, if a ball rolls off by one inch, you better get your table re-leveled. That's a bad roll off you have there.

Now there's the voice of logic.

 

[Cornerman]

Great explanation...reminds me of physics class way back when...and adding up x and y vectors...ack.

There you go. You've actually given yourself the best answer. It's vector addition.

Fred

 

[Jude Rosenstock]

( I see that Bob beat me to it with a much more complete answer)

The other explanations are essentially correct. The scientific explanation has to do with time. Assuming the exact same shot line, the force of gravity is the same along that line and is independent of the speed of the shot. What's different is that for the fast shot, gravity is in effect for a shorter time, resulting in less deflection than a slower shot.

Now, just for fun, to see if you understood Bob's post, here's the test question:

If you fire a bullet on a perfectly level trajectory, it will eventually land on the ground (provided it doesn't hit anything first). If you drop a bullet at exactly the same time from the same height as the gun, which bullet will hit the ground first?

Tom

This is exactly correct. The rate of gravity is about 10 meters/sec/sec. That is to say, horizontal force plays no impact on how quickly an object falls so as Tom points out, a falling object that has horizontal force applied will fall at the exact same rate as an object with 0 horizontal force applied.

In reference to the table with a roll, this means that your cueball will roll off at the same rate of time, not distance. Two balls traveling for the same amount of time will have similar deviation from the intended course so striking the ball harder will create less deviation from the table roll than a slow hit cueball.

 

[jay helfert]

The Dennis Miller Show

If any of you watched the old Dennis Miller show that was on HBO for years, you may have noticed in the opening sequence six balls that looked like little "Earths" going into six pockets on a pool table. The song "Everybody Wants To Rule The World" was playing in the background while this shot was being made.

Well, I made that shot for Dennis. It was done by using six cue balls painted to look like planet Earth. And it was made on a movie prop "pool table". This table had a plywood surface covered with plain green cloth. To say it rolled off is a massive understatement. The balls literally rolled everywhere in every direction.

I tried the shot a few times and told them it was nearly impossible to make this shot. Balls were rolling everywhere. I said there may be one way for me to do it. I have to shoot REAL hard! That way there is little, if any, roll off before they reach the pockets. The Director said go ahead and try it. I shot it six times with full force and twice I made all six balls/Earths. And I mean I hit it really hard!

Just like that, we were done with my segment. When it aired on TV, they slowed down the film speed considerably, so you could see the balls rolling into the holes. Ah, the wonders of Hollywood! Of course, they substituted Dennis for me, and made it look like he made the shot. I enjoyed hanging out with Dennis that day. He's a cool guy and very bright.

 

[Balabushka]

Bottom line, if a ball rolls off by one inch, you better get your table re-leveled. That's a bad roll off you have there.

LOL! Common sense just slammed a rock on the scissors of science.

 

[jason]

Newton's First Law:
An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

The force of gravity pushes down on the ball to the table. With enough of an angle on the table and/or a smooth enough surface, the balls would just go to one side of the table. Friction from the cloth and the ball help to hold them together. Try a marble on you kitchen room table and a slight angle.

There is another factor that hasn't been mentioned. Not all balls are prefectly round or weighted evenly. This could also cause the ball to roll off. And then there is the lint or chalk...but this never happens to JA!