A radio transmission tower has a mass of 80 kg and is 12 m high. The tower is anchored to the ground by a flexible joint at its base, but it is secured by three cables 120° apart (Fig. 11–50). In an analysis of a potential failure, a mechanical engineer needs to determine the behavior of the tower if one of the cables broke. The tower would fall away from the broken cable, rotating about its base. Determine the speed of the top of the tower as a function of the rotation angle θ. Start your analysis with the rotational dynamics equation of motion d L → / d t = τ → net . Approximate the tower as a tall thin rod. FIGURE 11–50 Problem 80.
A radio transmission tower has a mass of 80 kg and is 12 m high. The tower is anchored to the ground by a flexible joint at its base, but it is secured by three cables 120° apart (Fig. 11–50). In an analysis of a potential failure, a mechanical engineer needs to determine the behavior of the tower if one of the cables broke. The tower would fall away from the broken cable, rotating about its base. Determine the speed of the top of the tower as a function of the rotation angle θ. Start your analysis with the rotational dynamics equation of motion d L → / d t = τ → net . Approximate the tower as a tall thin rod. FIGURE 11–50 Problem 80.
A radio transmission tower has a mass of 80 kg and is 12 m high. The tower is anchored to the ground by a flexible joint at its base, but it is secured by three cables 120° apart (Fig. 11–50). In an analysis of a potential failure, a mechanical engineer needs to determine the behavior of the tower if one of the cables broke. The tower would fall away from the broken cable, rotating about its base. Determine the speed of the top of the tower as a function of the rotation angle θ. Start your analysis with the rotational dynamics equation of motion
d
L
→
/
d
t
=
τ
→
net
. Approximate the tower as a tall thin rod.
12–163. The car travels along the circular curve having a
radius r = 400 ft. At the instant shown, its angular rate of
rotation is ở = 0.025 rad/s, which is decreasing at the rate
ö = -0.008 rad/s². Determine the radial and transverse
components of the car's velocity and acceleration at this
instant and sketch these components on the curve.
*12–164. The car travels along the circular curve of radius
r = 400 ft with a constant speed of v = 30 ft/s. Determine
the angular rate of rotation ở of the radial line r and the
magnitude of the car's acceleration.
r= 400 ft
(II) Two masses, mA = 35.0 kg and mB = 38.0 kg, are
connected by a rope that hangs
over a pulley (as in Fig. 10-59).
The pulley is a uniform cylinder of
radius 0.381 m and mass 3.1 kg.
Initially ma is on the ground and
mB rests 2.5 m above the ground.
If the system is released, use
conservation of energy to deter-
mine the speed of mB just before
it strikes the ground. Assume the
pulley bearing is frictionless.
%3D
RO
mB
mA
2.5 m
FIGURE 10-59
ba
Problem 67.
inoni lo
(IID) A.
17-106. The truck carries the spool which has a weight of
500 Ib and a radius of gyration of kg = 2 ft. Determine the
angular acceleration of the spool if it is not tied down on the
truck and the truck begins to accelerate at 3 ft/s². Assume
the spool does not slip on the bed of the truck.
Chapter 11 Solutions
Physics for Scientists and Engineers with Modern Physics
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