8. Consider a cantilever viewing platform extending over the rim of a cliff as shown below. In an unsafe situation, the platform would pivot about the cliff's edge. Without fixing bolts, what is the maximum mass capacity m of the platform? L x R = 1/2/22 - x mg xy The following quantities are assumed known: L (m), M (kg), m (kg), and x (m). The gravity force Mg acts in the middle of the platform. The platform thickness can be neglected. The ground force N is vertical but has unknown magnitude. In the limiting case where the platform starts to pivot about the cliff's edge, d = 0. (a) Find the magnitude of N in the safe situation using the fact that the net force exerting on the platform is zero (equilibrium of forces). (b) Write the moments of force about the cliff's edge for all the forces shown in the figure in the safe situation where d > 0. (c) Find the maximum mass capacity m for which the platform becomes unsafe using the fact that the net moment exerting on the platform is zero (equilibrium of moments when d = 0 and the platform is still just horizontal).
8. Consider a cantilever viewing platform extending over the rim of a cliff as shown below. In an unsafe situation, the platform would pivot about the cliff's edge. Without fixing bolts, what is the maximum mass capacity m of the platform? L x R = 1/2/22 - x mg xy The following quantities are assumed known: L (m), M (kg), m (kg), and x (m). The gravity force Mg acts in the middle of the platform. The platform thickness can be neglected. The ground force N is vertical but has unknown magnitude. In the limiting case where the platform starts to pivot about the cliff's edge, d = 0. (a) Find the magnitude of N in the safe situation using the fact that the net force exerting on the platform is zero (equilibrium of forces). (b) Write the moments of force about the cliff's edge for all the forces shown in the figure in the safe situation where d > 0. (c) Find the maximum mass capacity m for which the platform becomes unsafe using the fact that the net moment exerting on the platform is zero (equilibrium of moments when d = 0 and the platform is still just horizontal).
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Transcribed Image Text:8. Consider a cantilever viewing platform extending over the rim of a cliff as shown below. In an
unsafe situation, the platform would pivot about the cliff's edge. Without fixing bolts, what is
the maximum mass capacity m of the platform?
L
x
R = 1/2/22 - x
mg
xy
The following quantities are assumed known: L (m), M (kg), m (kg), and x (m). The gravity
force Mg acts in the middle of the platform. The platform thickness can be neglected. The
ground force N is vertical but has unknown magnitude. In the limiting case where the platform
starts to pivot about the cliff's edge, d = 0.
(a) Find the magnitude of N in the safe situation using the fact that the net force exerting on
the platform is zero (equilibrium of forces).
(b) Write the moments of force about the cliff's edge for all the forces shown in the figure in
the safe situation where d > 0.
(c) Find the maximum mass capacity m for which the platform becomes unsafe using the
fact that the net moment exerting on the platform is zero (equilibrium of moments when
d = 0 and the platform is still just horizontal).
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