A 50kg safe made of steel rests on a steel floor. A spring with a spring constant of 550 N/m is attached to the side of the safe and then stretched out to the right. If the spring starts out 1m long, how long will it stretch to before the safe moves? Draw a free body diagram and solve.

It will stretch 66 [cm]

Explanation:

In order to solve this problem, we must understand that there is movement between the safe and the steel floor, that is, there is a force of friction between surfaces. Since the value of static coefficient of friction between steel surfaces is not given, we must perform an Internet search in order to find an approximate value of this value.

μ = 0.74

In the attached image we can find the free body diagram with the forces interacting on the safe.

First we perform a summation of forces on the Y axis equal to zero, in this way we can find the value of the normal force, which will be needed later.

Then we perform a summation of forces on the X axis equal to zero, in order to find the equation that relates the frictional force with the elastic force of the spring.

Knowing that the friction force is equal to the product of the normal force by the coefficient of friction we can find the elastic force.

The elastic force in a spring is equal to:

Fe = k*x

Clearing x

x = 362.97 / 550

x = 0.66 [m] or 66 [cm]

Note: In the attached image we can see the free body diagram with the forces acting over the safe.

the results is a decrease in air temperature with an increase of altitude.

explanation:

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.