A uniform ladder with mass m2 = 14kg and length L = 3.2m rests against a smooth wall. A do-it-yourself enthusiast of mass m₁ = 70kg stands on the ladder a distance d = 1.2m from the bottom (measured along the ladder.) There is no friction between the wall and the ladder, but there is a frictional force, with µ = 0.25, between the floor and the ladder. N₁ is the magnitude of the normal force exerted by the wall on the ladder, and N₂ is the magnitude of the normal force exerted by the ground on the ladder. What angle 6, will cause the static friction with the floor to be maximized? Will the ladder start to slip when the angle is made larger, or smaller than this borderline value?

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A board sits in equilibrium. On the left end, there is a wire that supports the board from the ceiling, and to the right, there is a sawhorse that supports the board from the ground. The sawhorse is a distance d= 1/5l from the right edge of the board. There is a block with mass ms= 4.5kg that is a distance 3/4l from the right edge of the board. Finally the board has a mass mb= 11kg. c) Write down Newton's 2nd law. Put the equation in terms of mb, ms, g, T, and Fn. Where T is the tension in the wire, and Fn is the normal force of the sawhorse on the board. d) Write down Newton's 2nd Law for rotations. Put the equation in terms of l, mb, ms, g, T, and Fn.

Question 2 A rope of length L = 2.8 m and mass m = 2 kg is initially at rest and can slide on an inclined surface with incline = 20° as shown in the figure. Assume that the part of the rope that is not on the inclined surface hangs down vertically at all times and that the static friction coefficient between the rope and the surface is μ = 0.49. 0 b a) Calculate the maximum value of b for which the rope will not start sliding down the slope.

The mB = 8 kg block is moving to the right with a velocity of vo = 0.96 mls on a horizontal surface when a force P is applied to it at time t = 0 as shown in the following figure. The coefficient of kinetic friction between the block and the surface is Hk = 0.27. Use P = 38, P2 = 72, t1 = 0.15, t2 = 0.35. %3D Р, N P2 P mB P1 t, s t1 t1 Calculate the velocity v in m/s of the block when t = 0.35 s. Insert your answer correct up to at least a third decimal place.

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A block of mass M = 109.0 kg on an inclined plane is attached to another block of mass m via a string, as in the figure below. The coefficients of static and kinetic friction for the block and the incline are u, = 0.40 and uy = 0.20 and the plane is inclined 16.9° with horizontal. (a) Determine the range of values for m, the mass of the hanging block, for which the block will not move unless disturbed, but if nudged, will slide down the incline. 73.4 kg s m s.03 kg (b) Determine a range of values for m for which the block will not move unless nudged, but if nudged will slide up the incline. 52.94 kg s m s 10.82 kg eBook

A rope of Length L = 3m and mass m= 3Kg is initially At rest and can slide on an inclined surface with Inclined theta = 15° as shown in the figure. Assume that the part of the rope that is not on the Inclined surface hanges down vertically at all times and that the static friction coefficient between the rope and the surface is MUs = 0.36 a) calculate the maximum value of b for which the rope will NOT start sliding down the slope. Assume that b = 0.33m and that the coefficient of kinetic friction between the rope and the Inclined surface is MUk = 0.27. Let y (in metres) be the distance travelled by the rope after it has been released from rest.  b) calculate the initial acceleration of the rope  Calculate the work done by gravity as a function of y  c) calculate the work done by the friction force as a function of y Hence calculate the velocity of the rope at the moment the rope has just completely left the Inclined surface