1An 8.0 m, 200 N uniform ladder rests against a smooth wall. The coefficient of
ID: 2258137 • Letter: 1
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1An 8.0 m, 200 N uniform ladder rests against a smooth wall. The coefficient of static friction between the ladder and the ground is 0.55, and the ladder makes a 50.0
An 8.0 m, 200 N uniform ladder rests against a smooth wall. The coefficient of static friction between the ladder and the ground is 0.55, and the ladder makes a 50.0 degree angle with the ground. How far up the ladder can an 880 N person climb before the ladder begins to slip? Note: a few of you will encounter an odd bug in this problem. The random numbers WebAssign generates for you may say the person can climb, say, 11.5m up a ladder that's only 11m long. If that happens, just input 11.5m as your answer and the system should accept it. m A 480 N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00 m long, uniform, 120 N rod as indicated in Figure P8.17. The left end the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0 degree angle with the vertical. Find the tension, T, in the cable. Find the horizontal and vertical components of force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions.)Explanation / Answer
1)The three vertical forces are
200 N
880 N
1080N (normal force acting up on the floor)
Since the upward forces = sum of the downward forces.
The horizontal forces are
Frictinal force = 0.55 * 1080 = 594
The normal reaction force on the wall = frictional force = 594 N . Since Horizontally the sum of the forces is zero
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The moment about the foot of the ladder must be zero.
200* 4 cos 50 + 880 * d cos 50 - 594 *8 sin 50 = 0
d = from the bottom
2 (a) to find tension in cable:
torque from tension = torque from weight of sign + weight of rod
T *6.00* sin60 = 480 * 4 + 120 * 3
T = 438.786 N
(b) horiz component from hinge = horiz component of tension
horiz component from hinge = 438.786 * sin30 = 219.393 N
vertical components
V + 438.786(cos 30) - 480 - 120 = 0
V=220 N
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