**Problem : **
A rocket taking off from the earth is accelerating straight upwards at
6.6 m/sec^{2}. How long will it take an apple of 0.2 kilograms to hit the floor
of the rocket if it is dropped from a height of 1.5 meters?

The effective gravity in the spaceship is given by the gravity on earth plus the
gravity due to the upward acceleration of the rocket:

*g*_{eff} = 6.6 + 9.8 = 16.4 m/sec

^{2}. The time taken for an object to reach the ground can be
determined from Galileo's kinematic equation which asserts that

*x* = 1/2*gt*^{2}, and thus

*t* = = 0.43 secs.
Of course the mass of the apple is irrelevant.

**Problem : **
If you measure the speed of light on earth, will the result be the same as of
you measured it in interstellar space, far from any gravitational fields?

Einstein's principle of equivalence demands that all measurements of the speed
of light be the same. Imagine a spaceship in free-fall in a gravitational
field, such that it is instantaneously at rest (it has not started to fall yet).
There is effectively no gravity in these spaceships. The principle of
equivalence demands that there be no method of determining whether they are
falling or in a gravitational field, so it must be the case that an experiment
to determine the speed of light will give the same result as if the experiment
was performed far from any gravitational field.

**Problem : **
If wood was found to fall at a different rate to plastic (*ie.**g*_{wood}*g*_{plastic} ), what would be the consequences for the principle of
equivalence?

If this was found to the true, the principle of equivalence would no longer
hold. It was shown (see

Inertial and Gravitational
Masses that the gravitational mass was
equivalent to the inertial mass if and only if

*g*_{wood} = *g*_{plastic}, and
that the same was true for all other materials.

**Problem : **
A mass *M* is at the origin. Two masses *m* are at points (*R*, 0) and
(*R* + *x*, 0) where *x* < < *R*. What is the difference in the gravitational
force on the two masses? This is the longitudinal tidal force. (Hint:
make some approximations)

The force is given by Newton's Universal Law:

The second equality omitted the term in

*x*^{2}. Then using a binomial
expansion we have:

**Problem : **
Again, a mass *M* is at the origin. Now, two masses are at (*R*, 0) and
(*R*, *y*), where *y* < < *R*. What is the difference in the gravitational
force on the two masses, and what is its effect? This is the
transverse tidal force.

To second order in

(*y*/*R*), both masses are equally distant from the
origin, and the magnitude of the force is essentially the same. The
direction of the forces, however, differs in first order

(*y*/*R*). In
fact, this difference is the

*y*-component of the force on the top
mass:

The difference points along the line joining the masses and acts to
pull the masses together. The combination of longitudinal and
tranverse tidal forces causes water on the side of the earth closest to
the moon to be pulled towards it. Water on the opposite side from the
moon is repelled (from the moon, causing it to bulge away from the
earth, and water in between is pulled towards the center of the earth.