Douglas Adams physics question .

EoghanIRL

According to the late Douglas Adams (Hitchiker's Guide to the Galaxy), there is a restaurant at the end of the universe. Suppose a diner there dropped a fork towards Earth. Pretend that there is nothing else in the Universe. With what speed will this object hit the Earth's surface. Assume the object is infinitely far away from Earth, has nearly zero speed and thus has zero potential energy before it is dropped.

I've been trying to figure it out but I seem to be missing something.

Ek is zero which means mgh is zero
S is infinity.
I understand that loss in Ek is gain in Ep and vica versa.
So v^2 = 2gh
But you are weightless in space so g is zero . gravitational force is constant I suppose because there is nothing else in the universe besides earth fork and dinner.
V is nearly zero so I let it equal 1/infinity.
S is infinity .

What am I missing .thanks

dulpit

EoghanIRL wrote: »

What am I missing

The restaurant at the end of the universe is at the end of time, not the physical end of the universe. It's a time being referred to, not place.

Choochtown

The force experienced due to the gravitational pull of the earth is proportional to 1 divided by distance squared. So if distance is infinity it makes the force due to gravity infinitely small i.e. =0 .

However if the object is moving towards the earth with any velocity however small it will continue to move as there is nothing to stop it. In theory as it gets closer and closer to earth it will experience more and more of a gravitational pull. This is of course assuming that there is nothing else in the universe to attract it.

Turtwig

EoghanIRL wrote: »

According to the late Douglas Adams (Hitchiker's Guide to the Galaxy), there is a restaurant at the end of the universe. Suppose a diner there dropped a fork towards Earth. Pretend that there is nothing else in the Universe. With what speed will this object hit the Earth's surface. Assume the object is infinitely far away from Earth, has nearly zero speed and thus has zero potential energy before it is dropped.

I've been trying to figure it out but I seem to be missing something.

Ek is zero which means mgh is zero
S is infinity.
I understand that loss in Ek is gain in Ep and vica versa.
So v^2 = 2gh
But you are weightless in space so g is zero . gravitational force is constant I suppose because there is nothing else in the universe besides earth fork and dinner.
V is nearly zero so I let it equal 1/infinity.
S is infinity .

What am I missing .thanks

It's more a case of how you approached this. Let's start with what you know. This potential energy of the fork falling towards earth is given by
[latex]U = -\frac{ GM_{\left(Earth \right)}*m_{\left( fork \right)} } {R}.
[/latex]

R here is infinity so you can assume the potential energy U to be zero. The object starts at rest so we can assume the Kinetic Energy K is also zero.

As the fork falls towards earth it will gain kinetic energy. Since we are assuming there is nothing else in the Universe affecting the fork, this kinetic energy will have some relationship to the potential energy. Think, conservation of energy. The total energy of the system E must be zero.
[latex]E = 0[/latex]

What you're looking for is a description for E in terms of the kinetic Energy and Potential Energy at a distance equal to the radius of the earth. This will be when the fork 'impacts' the earth.
Hope this helps.

If you want then for fun do it for an asteroid [latex]1 x 10^{15}\, kg[/latex] hitting the earth.