physics

A ladder (ℓL = 7.50 m) of weight WL = 350 N leans against a smooth vertical wall. The term "smooth" means that the wall can exert only a normal force directed perpendicular to the wall and cannot exert a frictional force parallel to it. A firefighter, whose weight is 886 N, stands 6.50 m up from the bottom of the ladder (this distance goes along the ladder, it is not the vertical height). Assume that the ladder's weight acts at the ladder's center, and neglect the hose's weight. What is the minimum value for the coefficient of static friction between the ladder and the ground, so that the ladder (with the fireman on it) does not slip? (Assume θ = 51.0°.)

  1. 👍 0
  2. 👎 0
  3. 👁 1,548
  1. There are only two horizontal forces in this problem, at the wall and at the ground.
    Therefore they are equal and opposite, call the magnitude F

    now balance vertical forces
    886 + 350 = force down = 1236 N
    that is therefore the normal force up
    at the ladder base
    the max friction force is thus
    1236 mu
    now take moments about top of ladder
    clockwise:
    1236 * 7.5 cos 51
    counterclockwise
    1236 mu *7.5 sin 51 + 350 *3.75 cos 51 + 886 *1*cos 51
    set those equal and solve for mu
    by the way look at the old questions answered below

    1. 👍 0
    2. 👎 1

Respond to this Question

First Name

Your Response

Similar Questions

  1. Pre-Calculus

    A ladder leans leans against a building that has a wall slanting away from the ladder at an angle of 96 degrees with the ground. If the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up

  2. Pre-Cal

    A 13-ft ladder leans against a building so that the angle between the ground and the ladder is 63 degrees. How high does the ladder reach on the building? (round your answer to the nearest foot)

  3. math

    A ladder 29 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed

  4. physics help!

    A uniform stationary ladder of length= 5.1 m and mass= 15 kg leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. The coefficient of static friction between floor and ladder is μ = 0.41.

  1. Trig

    A 12 foot ladder leans against a building. The top of the ladder leans against the wall 10.5 feet from the ground. What is the angle formed by the ground and the ladder? Assume its a right triangle.

  2. Maths

    A ladder leans against a vertical wall of height 12m.if the foot of the ladder is 5m away from the wall,calculate the length of the ladder.

  3. math

    A ladder is 13.0m long. It leans against the wall. The base of the ladder is 3.7m from the wall. What is the angle of inclination of the ladder to the nearest tenth of a degree?

  4. math

    a fire fighter's 36 foot ladder leans against a building. the top of the ladder touches the buliding 28 ft above the ground. what is the measure of the angle of the ladder forms with the ground?

  1. statics/physics

    The uniform 10-kg ladder in the figure rests against the smooth wall at B, and the end A rests on the rough horizontal plane for which the coefficient of static friction is 0.3. determine the angle of inclination of the ladder and

  2. math

    A - 12 ladder leans against the side of a house. The bottom of the ladder is 9ft from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.

  3. Physics

    In the figure, a uniform ladder of weight 200 N and length 10 m leans against a perfectly smooth wall. A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of static friction between the ladder and the

  4. geometry

    the triangles formed by two ladders leaning against a wall are similar. how long is the shorter ladder? the first ladder is 42ft and leans against the wall at 24ft, and the shorter ladder leans against the wall at 8ft.

You can view more similar questions or ask a new question.