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Impact of Deployment Timing on Flight Performance

Figures (9)

DANDE drag equation
Figure 6.10 Frictional forces, such as f→,f→, always oppose motion or attempted motion between objects in contact. Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view. For the object to move, it must rise to where the peaks of the top surface can skip along the bottom surface. Thus, a force is required just to set the object in motion. Some of the peaks will be broken off, also requiring a force to maintain motion. Much of the friction is actually due to attractive forces between molecules making up the two objects, so that even perfectly smooth surfaces are not friction-free. (In fact, perfectly smooth, clean surfaces of similar materials would adhere, forming a bond called a “cold weld.”)
Figure 6.11 (a) The force of friction f→f→ between the block and the rough surface opposes the direction of the applied force F→.F→. The magnitude of the static friction balances that of the applied force. This is shown in the left side of the graph in (c). (b) At some point, the magnitude of the applied force is greater than the force of kinetic friction, and the block moves to the right. This is shown in the right side of the graph. (c) The graph of the frictional force versus the applied force; note that fs(max)>fk.fs(max)>fk. This means that μs>μk.μs>μk.
Figure 6.12 Artificial knee replacement is a procedure that has been performed for more than 20 years. These post-operative X-rays show a right knee joint replacement. (credit: modification of work by Mike Baird)
Figure 6.13 (a) A crate on a horizontal surface is pushed with a force P→.P→. (b) The forces on the crate. Here, f→f→ may represent either the static or the kinetic frictional force.
Figure 6.14 The motion of the skier and friction are parallel to the slope, so it is most convenient to project all forces onto a coordinate system where one axis is parallel to the slope and the other is perpendicular (axes shown to left of skier). The normal force N→N→ is perpendicular to the slope, and friction f→f→ is parallel to the slope, but the skier’s weight w→w→ has components along both axes, namely w→yw→y and w→x.w→x. The normal force N→N→ is equal in magnitude to w→y,w→y, so there is no motion perpendicular to the slope.
Figure 6.15 Two rough surfaces in contact have a much smaller area of actual contact than their total area. When the normal force is larger as a result of a larger applied force, the area of actual contact increases, as does friction.
Figure 6.16 The tip of a probe is deformed sideways by frictional force as the probe is dragged across a surface. Measurements of how the force varies for different materials are yielding fundamental insights into the atomic nature of friction.
Figure 6.17 (a) Each block moves at constant velocity. (b) Free-body diagrams for the blocks.

Deployment timing affects how well a parachute slows a falling object. This means the parachute must work harder to slow it down. Parachutes work by creating drag, which is a force that pushes against the falling object.

The faster the object is moving when the parachute opens, the more drag is created. This drag helps reduce the object's speed until it reaches a steady, slower speed called terminal velocity. If the parachute opens at the right time, it can help the object reach this slower speed more quickly and safely.

The best result happens when the parachute opens at just the right time to balance speed and drag. It shows how the timing of the parachute opening can change how fast or slow the object falls.

Key Points

  • Terminal velocity is the maximum speed attainable by an object as it falls through a fluid when the sum of the drag force and buoyancy equals the downward force of gravity, resulting in zero acceleration.
  • Drag force is the force experienced by an object moving through a fluid, calculated using the drag equation which depends on the fluid's density, the object's velocity, the drag coefficient, and the object's reference area.
  • Air resistance is the force that opposes the motion of an object through the air, and it increases with the square of the object's velocity, affecting the object's acceleration and terminal velocity.

Terms

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