...Find the magnitude of the normal reaction and of the frictional force at the ground.?

Question

A uniform ladder of mass 30kg and length 10m has its base resting on rough horizontal ground and its top against a smooth vertical wall. The ladder rests in equilibrium, at 60 degrees to the horizontal, with a man of mass 90kg standing on the ladder at a point 7.5m from its base. Find the magnitude of the normal reaction and of the frictional force at the ground.

The answers: 1176N, 467N respectively.

I thought I worked out an answer, but I somehow got 1250N (or something along those lines) for my normal reaction, and my working isn't all that plausible, really, so- any help'll be greatly appreciated! Thanks. :)

Answer 1

You're dealing with 2-dimensional equilibrium, so the sum of the forces in the vertical direction and the sum of the forces in the horizontal direction have to be equal to 0.

The ladder is leaning on a vertical frictionless wall. So, there is no vertical force between the ladder and the wall. The ladder on the wall will only have a horizontal component to it.

There are three vertical forces in the system, namely the weight of the man (90*9.81=882.9N), the weight of the ladder (30*9.81=294.3N) and the normal force of the ladder on the ground. The two weight forces are acting downward, so the normal force of the ladder is acting upward. This force is equal to 882.9+294.3=1177.2N (close enough due to rounding)

There are only 2 horizontal forces in the system, namely the friction of the ladder on the ground and the horizontal force of the ladder on the wall. To find the force of the ladder on the wall, you need to sum moments about the contact point of the ladder on the ground. If you solve the geometry of the triangle made by the wall, ladder and ground, you see that the weight of the ladder acts 2.5m from the pivot, the weight of the man acts 3.75m from the pivot, and the ladder touches the wall 8.7m above the ground. So, you get:
[(2.5*294.3) + (3.75*882.9)] / 8.7 = 465.1N

Hope this helps.

Answer 2

Your the two queries are genuine. specific, you're precise if curler have been to be pulled purely by 250 N rigidity it does not holiday with consistent velocity. the very fact it is been informed that that's moving with consistent velocity, potential there is another rigidity performing to oppose this rigidity. What that is, you're able to desire to wager. yet while it has not been given does not propose which you have been informed that it does not exist. in this occasion you're able to desire to end that it would be the floor which will desire to be making use of a few rigidity. Now wherein direction floor can prepare rigidity. purely 2 dircetions primary to it and tangential to it. before you started pulling the curler, it develop into status there merrily even in spite of the undeniable fact that earth develop into pulling it in direction of the centre. this could take place because of the fact floor is confusing it delivers resistance to alter of its shape only as a spring does. yet what occurs in spring is seen, right here it is not seen. As a rsult of this floor applies equivalent and opposite rigidity on the curler in opposite direction. this is termed primary reaction.. Rememebr that this isn't mounted yet continually adjust to the situation. Now in case you push the curler horizontaly as gently as achievable. you're making use of a rigidity however the curler does not circulate, meaning floor is likewise able to making use of tangential rigidity, popularly familiar as frictional rigidity. This rigidity is likewise self-adjusting and that's continually equivalent to the utilized rigidity while the physique is completely at relax or moving in a right now line with consistent velocity. right here comes your next question. The rigidity of 250 N could be thoght as made up of two forces 250xsin30 = a hundred twenty five N alongside horizontal direction and 250xcos30 = 250x0.86 = 215 N alongside vertically upward direction. This reduces the rigidity appearing on the curler in direction of the centre of earth by 215 N and consequently additionally reduces the self-adjusting primary reaction by the floor. So now that's obvious that the tangental frictional rigidity which the floor is making use of on the curler interior the alternative direction of its action is a hundred twenty five N. the utmost frictional rigidity which a floor can prepare on a moving or tending to be moving merchandise, referred to as as proscribing friction is proportional to the conventional reaction. by pulling the curler instead of pushing it we cut back the conventional reaction and consequently the rigidity of proscribing friction. Your further queries are welcome