A uniform stationary ladder of length L = 5.3 m and mass M = 19 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. The ladder makes an angle θ = 59° with respect to the floor. A painter of mass 8M stands on the ladder a distance d from its base. a)Find the magnitude of the normal force N, in newtons, exerted by the floor on the ladder.  b)Find an expression for the magnitude of the normal force NW exerted by the wall on the ladder.  c)What is the largest distance up the ladder dmax, in meters, that the painter can stand without the ladder slipping?

A small box of mass m1m1 is sitting on a board of mass m2m2 and length LL (Figure 1). The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is μsμs μsμs   Throughout the problem, use gg for the magnitude of the free-fall acceleration. In the hints, use ff for the magnitude of the friction force between the board and the box. Find Fmin, the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box (which will then fall off of the opposite end of the board) Express your answer in terms of some or all of the variables μsμs m1m1 m2m2 g L Do not include ff in your answer.

A 14.0 m uniform ladder weighing 480 N rests against a frictionless wall. The ladder makes a 55.0°-angle with the horizontal. (a) Find the horizontal and vertical forces (in N) the ground exerts on the base of the ladder when an 850-N firefighter has climbed 4.10 m along the ladder from the bottom. horizontal force magnitude 342.35 direction vertical force magnitude direction towards the wall up m N ✪ N (b) If the ladder is just on the verge of slipping when the firefighter is 9.10 m from the bottom, what is the coefficient of static friction between ladder and ground? (c) What If? If oil is spilled on the ground, causing the coefficient of static friction to drop to half the value found in part (b), what is the maximum distance (in m) the firefighter can climb along the ladder from the bottom before the ladder slips?

An engineering student suspends his 300 N tool box by using a system of ropes and pulleys, as shown in the figure. The mass M1 is equal to 20.0 kg. The angle e and the mass M2 have been chosen so that the entire system remains at rest. Assume that the pulleys are all ideal and frictionless, and that the cords have negligible weight. A+y T2 M2 Mi TOOL BOX 33. The angle 0 is equal to A. 33.2°. В. 3.8°. C. 56.8°. D. 49.2°. E. 40.8°. 34. The mass M2 is equal to A. 30.6 kg. B. 20.0 kg. C. 40.0 kg. D. 50.6 kg. E. 36.6 kg.

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A loaded penguin sled weighing 61.0 N rests on a plane inclined at angle θ = 23.0° to the horizontal (see the figure). Between the sled and the plane, the coefficient of static friction is 0.260, and the coefficient of kinetic friction is 0.120. (a) What is the minimum magnitude of the force ?→�→, parallel to the plane, that will prevent the sled from slipping down the plane? (b) What is the minimum magnitude F that will start the sled moving up the plane? (c) What value of F is required to move the sled up the plane at constant velocity

A large crate is supported on wheels. The wheels can be locked into position to prevent rotation. The weight of the crate is 150 lb and the coefficient of static friction between the floor and the crate wheels is 0.35. A force P is applied as shown to move the crate to the right. If all the wheels are locked to prevent rotation, determine: a) The magnitude of force P required to move the crate to the right b) The largest value of height h to prevent the crate from tipping over. P A a -30%

When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure a. The total is supported by the force n exerted by the floor on the toes of one foot. A mechanical gravitational force on the body, F model of the situation is shown in Figure b, where T is the force exerted by the Achilles tendon on the foot and R is the force exerted by the tibia on the foot. Find the values of T, R, and 0 when F, = n = 770 N. (For 0, enter the smaller of the g' two possible values between 0° and 90°.) -Achilles tendon Tibia 15.0° 18.0 cm 25.0 cm a T = R = N = Submit Answer

A fence post of mass m = 8 kg supports a fence with three lengths of barbed wire. The bottom wire is a distance d = 0.35 m from the ground and each wire is a distance 0.35 m above the previous one. Each of these three wires has the tension on it. For this problem, assume that the force exerted by these wires is purely horizontal. An additional guy wire is used to keep the pole upright with a tension of Fa = 490 N. The guy wire attaches to the post at a point h = 0.86 m above the ground and makes an angle of θ = 45 with respect to the horizontal. Write an expression for the tension in any one of the three fence wires.  What is the normal force that the ground exerts upward on the post?