please show your work, will add more points if you get it correctly. A uniform l

Question

please show your work, will add more points if you get it correctly.

A uniform ladder of mass (m) and length (L) leans against a frictionless wall, see figure. If the coefficient of static friction between the ladder and the ground is 0.48, what is the minimum angle (q) between the ladder and the floor at which the ladder will not slip? degrees A solid disk rotates in the horizontal plane at an angular velocity of 0.043 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.17 kg.m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk? rad/s A 1310 N uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. A W = 1800 N crate hangs from the far end of the beam, (a) Calculate the magnitude of the horizontal component of the force that the wall exerts on the left end of the beam. N

Explanation / Answer

4)

sum torques about bottom

N*L*sin(theta) - m g L/2 cos(theta) = 0

N wall = m g cot(theta)/2

sum forces in the x

friction - Nwall = 0
friction = mg cot(theta)/2

sum forces in the y
N - mg = 0

0.48*mg = mg cot(theta)/2
cot(theta) = 2*0.49

theta = arcot(2*0.49)= 45.58 degrees


5)

conservation of angular momentum

I w = (I + mr^2) w

0.17*0.043 = (0.17 + 0.5*0.4^2) w

w=0.0292 rad/s

6)

a) sum torque about bottom


-1310*L/2*cos(30) - 1800*L*cos(30) + T*L*sin(80) = 0

T=2158.9 N

sum forces in the x

N - 2158.9*cos(50) = 0
N = 1387.8 N

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