Safe landin 2. The force causes the sides of the box to buckle and lose structural integrity 3. Air is pushed out of the box as the box is crushed 4. The box is fully flattened We now consider the physical processes at play in each of these stages Table 1 Nomenclature Property Symbol Units Potential energy density J/m Youngs modulus Strain in box walls none Stress in box walls P Tensile strength Ts P Total kinetic energy Total potential energ. Volume of cardboard in box walls Distance scale over which buckling is significant AH m Width of box Thickness of box walls m Height of box of the top face of the be Proportion of top face through which air escapes Velocity of stunt person m/s an velocity of expelled air Mass of stur Density of air Acceleration due to gravity, g=9.8m/s2 Stage 1: Force Applied A force F(t) is applied uniformly over the top surface. The walls of the box expand slightly, allowing the box to compress longitudinally (along the direction of the force). While this applied force is small enough (less than the force necessary to cause buckling), the box absorbs little of the force and transmits to the ground (or next layer of the box catcher) a large fraction of the applied force. The applied force increases until it is on the order of the bucklin orce(F(t)N FB). At this point, the box begins to buckle Stage 2: Box Buckles The walls crumple, the box tears, and the top of the box is pressed down Once the box has lost structural integrity, although the action of deforming the box may present some resistance the force that the box itself can withstand is greatly diminished Consider the pristine box being deformed by a force applied to its upper face. To counteract this force, the walls of the box expand in the transverseSafe Landings 221 2. The force causes the sides of the box to buckle and lose structural integrity. 3. Air is pushed out of the box as the box is crushed. 4. The box is fully flattened. We now consider the physical processes at play in each of these stages. Table 1. Nomenclature. Property Symbol Units Potential energy density v J/m3 Young’s modulus Y Pa Strain in box walls
none Stress in box walls S Pa Tensile strength TS Pa Total kinetic energy U J Total potential energy V J Volume of cardboard in box walls V m3 Distance scale over which buckling is significant ∆H m Width of box w m Thickness of box walls τ m Height of box m Surface area of the top face of the box A m2 Proportion of top face through which air escapes α — Velocity of stunt person us m/s Mean velocity of expelled air ua m/s Mass of stunt person (and vehicle, if any) m kg Density of air ρ kg/m3 Acceleration due to gravity, g = 9.8 m/s2 g m/s2 Stage 1: Force Applied A force F(t) is applied uniformly over the top surface. The walls of the box expand slightly, allowing the box to compress longitudinally (along the direction of the force). While this applied force is small enough (less than the force necessary to cause buckling), the box absorbs little of the force and transmits to the ground (or next layer of the box catcher) a large fraction of the applied force. The applied force increases until it is on the order of the buckling force (F(t) ∼ FB). At this point, the box begins to buckle. Stage 2: Box Buckles The walls crumple, the box tears, and the top of the box is pressed down. Once the box has lost structural integrity, although the action of deforming the box may present some resistance, the force that the box itself can withstand is greatly diminished. Consider the pristine box being deformed by a force applied to its upper face. To counteract this force, the walls of the box expand in the transverse