# God's golf club

The golf club problem was a throwaway – I didn’t expect it to have a long duration. I can’t resist the following plea and will give a formal answer (there is a much simpler way of doing it)

1. Russ Says:
November 15th, 2006 at 12:02 am eI was hoping someone would pipe up with the answer, because now it’s kind of bugging me. It would seem the standard high school physics doesn’t apply to infinitely massive golf clubs wielded by superbeings. Or if it does, the golf ball flies off at infinite speed and/or blows up in a blinding flash of energy (amounting to it’s mass times the speed of light squared).Put a nerd out of his misery here – what’s the answer?

Assume the club has mass M and velcity V and the ball is mass m and velocity v. Momentum must be conserved and, for an elastic collision, so must energy.
Initially:
Momentum: MV
Energy 0.5 M V*V
Afterwards:
Momentum MV’ + mv
Energy 0.5 M*V’*V’ + 0.5 m * v * v
We have the equations:
MV = MV’ + mv
M*V*V = M*V’*V’ + m*v*v
We can reduce the variables by using the ratio of masses (A=M/m) :
A(V – V’) = v
A*(V*V – V’*V’) = v*v
Two equations, 3 unknowns – you will come out with a ratio of velocities. Bit messy. Then let A tend to infinity. You should get a simple answer. Then see if you can find a simpler approach – look at it with a fresh viewpoint –
P.

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### 10 Responses to God's golf club

1. Noel OBoyle says:

Different frame of reference? 🙂

2. Russ says:

It seems my math skills died along with my physics.
I suppose if A tends to infinity, then V-V’ tends to zero. So v = A(V-V’) = (infinity)(zero) = 42 parsecs/minute

3. pm286 says:

(1) Yes.
(2) Choose some numbers for the variables and put them in a calculator. Also, try V=v…

4. pm286 says:

(3) Sorry – I meant M = m

5. pm286 says:

A(V – V’) = v
A*(V*V – V’*V’) = v*v
so get rid of V’
V’ = V – v/A
A*(V*V – (V-v/A)^2) = v*v
A*V*V – A(V*V + v*v/(A*A) – 2*V*v/A) = v*v
v*v/A – 2*V*v = v*v
v/A – 2 * V = v
v(1/A – 1) = 2*V
— I seem to have lost a minus somewhere – that’s the problem of typing into WordPress …
v(1-1/A) = 2*V
as M/M increases 1/A decreases so in the limit
v = 2*V
Now… think of a simple way of justifying that. You don’t have to do any maths

6. Russ says:

Bah!
I had it worked down to 2V by a few different routes, and assumed it was wrong, because it still doesn’t really make sense to me.
This is why I do organic chemistry and not physics.
Anyhow, it seems all somewhat moot, given the impossibility of an infinitely massive golf club moving at all. Also, wouldn’t even a really, really heavy golf club begin to exert gravitational force on the golf ball, and in the limit, an infinitely massive club attracts the ball with infinite force (I would call that shot a “Black-hole-in-one”)
But anyway, if you can spoonfeed me the simple justification for why an infinitely massive club, moving at V hits a golf ball off at 2V, I’d love to hear it and put the matter to rest.

7. pm286 says:

(6) Instead of an infinitely massive club assume a very massive train travelling at V. There is a smooth shiny plate of the front which hits a glofball suspended by a very thin piece of cotton. There is a fly sitting by the side of the plate watching. The fly does not know it is on a train. It does not know it is moving (there is no acceleration). Describe what happens from the point of view of the fly… (Noel got this)

8. Bill says:

To expand on Peter’s explanation: the fly sees a golf ball coming towards him at V, since he doesn’t know he’s moving and the ball is not. Given a perfectly elastic collision and an essentially infinite train/ball mass ratio, he must see the ball moving away from him at V after the impact — which, since he is moving at V as well, gives the ball a velocity of 2V.
(Obconfession: I did the algebra and messed it up horribly, subbing for v instead of V’. But, as usual with me, the answer makes sense once someone else solves the problem for me.)
This was fun, for weird nerdy values of fun!

9. Dimple Veloso says:

Bah!
I had it worked down to 2V by a few different routes, and assumed it was wrong, because it still doesn’t really make sense to me.
This is why I do organic chemistry and not physics.
Anyhow, it seems all somewhat moot, given the impossibility of an infinitely massive golf club moving at all. Also, wouldn’t even a really, really heavy golf club begin to exert gravitational force on the golf ball, and in the limit, an infinitely massive club attracts the ball with infinite force (I would call that shot a “Black-hole-in-one”)
But anyway, if you can spoonfeed me the simple justification for why an infinitely massive club, moving at V hits a golf ball off at 2V, I’d love to hear it and put the matter to rest.
nice blog
Regards
Dimple
http://medcall.com.au

10. chris says:

seems to me that infinitely massive golf clubs could not travel through space, much less strike a golf ball. mass and velocity are inversely proportional. seems to me that as M approaches infinity, velocity approaches 0. Photons have negligible mass, therefore can approach the speed of… light. similar to the concept of wind resistance defining the terminal velocity of a falling object, the mass of an object limits the maximum possible velocity of the object traveling through the vacuum