Anonymous

# how smart are you??

A 13 m ladder whose weight is 185 N is placed against a smooth vertical wall. A person whose weight is 953 N stands on the ladder a distance 3.5 m up the ladder. The foot of the ladder rests on the floor 2.99 m from the wall. Calculate the force exerted by the wall. Answer in units of N.

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• Anonymous

To answer this question, you need to balance the moment (or torque) of each force. The moment is calculated by finding the following:

force*the perpendicular distance away that the force acts.

So for the ladder, the weight of the ladder acts at the middle of the latter, pointing straight down. Using the point where the ladder touches the ground as the axis of rotation, the perpendicular distance to where the force acts is half the distance to the wall, or 2.99/2 meters. Use geometry to find the angle (call it alpha) from the ground to the ladder (inverse cosine of 2.99/13). Then you can find the distance from the axis of rotation to the person's weight. This distance is 3.5/tan(alpha). Then find how high up the wall the ladder touches the wall. This is how far the force of the wall acts from the axis of rotation. this distance is 13*sin(alpha).

Now you have all the information to solve the problem. THe moments have to all add up to zero to be in static equilibrium (nothing moves). Multiply each force by the distance to the axis of rotation. If the moment would produce a clockwise rotation, add it. If the moment produces a counterclockwise rotation, subtract it. You end up with an equation like this:

185N*(2.99/2)m+953N*(3.5/tan(alpha))m-X*(13*sin(alpha))m=0

Solve for X!

X= 106N

Hope that helps.

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• Physics gosh.

try using the equation Fnet=ma or just use the Fnet statement

i'm too lazy i just finished school

• i have no clue, but i would like to know the answer.