A uniform ladder whose length is 5.0 m and whose weight is 330 N leans against a frictionless vertical wall. The coefficient of static friction between the level ground and the foot of the ladder is 0.52. What is the greatest distance the foot of the ladder can be placed from the base of the wall without the ladder immediately slipping?

x = 3.6 [m]

Explanation:

This problem can be easily solved using a static analysis of forces acting on the ladder, taking into account the respective distances. For easy understanding, a free body diagram should be made.

We perform a sum of force on the X-axis equal to zero, to find that the force exerted by the wall is equal to the friction force on the floor.

Then we perform a summation of forces on the Y axis, to determine that the normal force exerted by the floor is equal to the weight of the ladder.

We know that the friction force is equal to the product of normal force by the coefficient of friction.

In this way, by relating the friction force to the equations deduced above we can find the force exerted by the wall.

Then we make a summation of moments around the base point of the ladder, the equation realized can be seen in the attached image.

In the last analysis we can find the relationship between the horizontal and vertical distance of the ladder, with respect to the wall and the floor.

Then with the complementary analysis of the Pythagorean theorem we can find another additional equation.

The result of the greater distance is 3.6 [m]

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.

grav potential energy