1. A 16.4-m length of hose is wound around a reel, which is initially at rest. T
ID: 1460175 • Letter: 1
Question
1. A 16.4-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.39 kg · m2, and its radius is 0.173 m. When the reel is turning, friction at the axle exerts a torque of magnitude 4.17 N · m on the reel. If the hose is pulled so that the tension in it remains a constant 27.5 N, how long does it take to completely unwind the hose from the reel? Neglect the mass of the hose, and assume that the hose unwinds without slipping.
2. A 1160-N uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. A W = 1820-N crate hangs from the far end of the beam. Using the data shown in the drawing, find the following.
(a) the magnitude of the tension in the wire
? N
(b) the magnitudes of the horizontal and vertical components of the force that the wall exerts on the left end of the beam
Explanation / Answer
1.The torque due to the tension is 27.5* 0.173 = 4.76 Nm so the net torque will be = -4.17+4.76 = 0.59 N.m.
As we know that the torque cause the angular acceleration and the torque = Inertia times the angular acceleration.
So angular acceleration = 0.59/0.39 = 1.51 rad/s^2
the angle that the reel rotates = 16.4/0.173 = 94.797 rad.
The time = sqrt(2*angle/ang.acceleration) = sqrt(2*94.797/1.51) =11.2 Sec.
2. The torque about the point where it touches the wall,
W*L*cos(30degree) - T*L*sin(80degree) +1160*(L/2)*cos(30degree) = 0;
T = (1820*cos(30)+1160*cos(30)/2 )/sin(80) = 2110.524 N.
The horizontal force = T cos(50) = 1356.61 N right
vertical force = 1363.24482 upward
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