1) if a pendulum clock keeps perfect time at the base of a mountain, will it also keep perfect time when it is moved to the top of the mountain? explain.
2)if a grandfather clock is running slow, how could we adjust the length of the pendulum to correct the time?
3)explain (a) how it is possible for a large force to produce only a small, or even zero, torque, and (b) how it is possible for a small force to produce a large torque.

1) No

Explanation:

The period of a pendulum is given by

where

L is the length of the pendulum

g is the acceleration due to gravity

The value of g, acceleration due to gravity, is not exactly the same in all locations of the Earth. In fact, its value is given by

where G is the gravitational constant, M is the Earth's mass, and r the distance of the point from the Earth's center. This means that at the top of a mountain, r is slightly larger than at the Earth's surface, so the value of g is slightly smaller at the top of the mountain, and therefore the period of the pendulum will also be different (it will be slightly longer than at Earth's surface).

2) We need to decrease the length of the pendulum

Again, the period is given by

(1)

If the clock is running slow, it means that its period T' is slightly longer than the expected period T: so, we need to shorten the period.

From eq.(1), we see that the period is proportional to the square root of the length of the pendulum, L: therefore, if the length increases the period increases, and if the length decreases, the period will decreases.

Here we want to shorten the period: therefore, according to the equation, we need to decrease the length of the pendulum.

3)

The torque of a force applied is given by

where

F is the magnitude of the force

d is the distance between the point of application of the force and the pivot point

is the angle between the direction of the force and d

So we have:

a) If we have a large force F, it is possible to produce a small torque by decreasing d, so by applying the force really close to the pivot, or by decreasing , which means applying the force as more parallel as possible to d. The torque will be even zero if d=0 (force applied at the pivot point) or if (force parallel to d)

b) if we have a small force F, it is possible to produce a large torque by increasing d, so by applying the force really far to the pivot, or by increasing , which means applying the force as more perpendicular as possible to d.

i think the answer is a, hope this is right, that would be my best guess.

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account.   she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem.   she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem.   her desire for the new hairstyle is in conflict with her honesty and integrity.

d.   if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it.   the amount she has in her account is not the problem.   and if i may suggest, she might as well close her checking account, and put the money where it'll work for her.   it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now.   under no circumstances should he ask for a higher limit.

b.   he can ask for the grace period to be extended.   but that's no solution, the bank will almost certainly refuse anyway, and there are much better options.   he knew the rules of his credit card when he started using it.

c.   he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d.   he definitely should pay the minimum otherwise they could shut down his card.   he should also pay as much more as he possibly can.   he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices.   what he has to do:   pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.