Problem 5 Stability Small floating devices such as kayaks are marginally stable to lateral perturbations. We are inter- ested in designing a submerged kayak for a target user weighing mp = 60 kg. When seated in the kayak, the entire kayak is submerged just under the waterline (Fig 5) and the center of gravity of the user is at G. For your calculations, consider the kayak to be a cylinder with a radius of rk and of uniform density Pk. The kayak has a depth of dk. mp 5 NG D Pk TK d Ps r Figure 5: Cylindrical kayak with a one-sided stabilizer float. hc = 0.5 m, r = 1m, dk = 3m, ds 0.5 m. = To stabilize the kayak, a one-sided cylindrical stabilizer float of density ps, depth ds and radius rs is considered. The stabilizer float is exactly half submerged with the user on board. (1) Determine the density of the kayak PR and the stabilizer float p, so that the system floats in the given configuration (Fig 5). Assume the connector of length d has negligible mass. (2) Find the dimensions of stabilizer float attachment (d and rs) such that the system is stable to small lateral perturbations (rotation about the point C) in both directions. Hint: Calculate all moments about point O. To determine the stabilizer float parameters, consider the maximum and minimum contribution from the buoyancy forces of the stabilizer float as the kayak undergoes small rotation about point C.
Problem 5 Stability Small floating devices such as kayaks are marginally stable to lateral perturbations. We are inter- ested in designing a submerged kayak for a target user weighing mp = 60 kg. When seated in the kayak, the entire kayak is submerged just under the waterline (Fig 5) and the center of gravity of the user is at G. For your calculations, consider the kayak to be a cylinder with a radius of rk and of uniform density Pk. The kayak has a depth of dk. mp 5 NG D Pk TK d Ps r Figure 5: Cylindrical kayak with a one-sided stabilizer float. hc = 0.5 m, r = 1m, dk = 3m, ds 0.5 m. = To stabilize the kayak, a one-sided cylindrical stabilizer float of density ps, depth ds and radius rs is considered. The stabilizer float is exactly half submerged with the user on board. (1) Determine the density of the kayak PR and the stabilizer float p, so that the system floats in the given configuration (Fig 5). Assume the connector of length d has negligible mass. (2) Find the dimensions of stabilizer float attachment (d and rs) such that the system is stable to small lateral perturbations (rotation about the point C) in both directions. Hint: Calculate all moments about point O. To determine the stabilizer float parameters, consider the maximum and minimum contribution from the buoyancy forces of the stabilizer float as the kayak undergoes small rotation about point C.
International Edition---engineering Mechanics: Statics, 4th Edition
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Chapter8: Centroids And Distributed Loads
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Transcribed Image Text:Problem 5 Stability
Small floating devices such as kayaks are marginally stable to lateral perturbations. We are inter-
ested in designing a submerged kayak for a target user weighing mp = 60 kg. When seated in the
kayak, the entire kayak is submerged just under the waterline (Fig 5) and the center of gravity of
the user is at G. For your calculations, consider the kayak to be a cylinder with a radius of rk and
of uniform density Pk. The kayak has a depth of dk.
mp
5
NG
D
Pk
TK
d
Ps
r
Figure 5: Cylindrical kayak with a one-sided stabilizer float. hc = 0.5 m, r = 1m, dk = 3m, ds
0.5 m.
=
To stabilize the kayak, a one-sided cylindrical stabilizer float of density ps, depth ds and radius rs
is considered. The stabilizer float is exactly half submerged with the user on board.
(1) Determine the density of the kayak PR and the stabilizer float p, so that the system floats in
the given configuration (Fig 5). Assume the connector of length d has negligible mass.
(2) Find the dimensions of stabilizer float attachment (d and rs) such that the system is stable
to small lateral perturbations (rotation about the point C) in both directions.
Hint: Calculate all moments about point O. To determine the stabilizer float parameters,
consider the maximum and minimum contribution from the buoyancy forces of the stabilizer
float as the kayak undergoes small rotation about point C.
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