5.Force&Motion_II

5.Force&Motion_II

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Unformatted text preview: agnitude of fk is f k , max = µ k FN θ µk coefficient of kinetic friction The Department of Physics, CUHK The Department of Physics, CUHK 7 §4. The drag force and terminal speed 8 The drag force and terminal speed r D A fluid is anything can flow. When there is a relative velocity between a drag fluid and a body, the body experiences a drag force D that opposes the relative motion and points in the direction in which the fluid flows relative to the body. r Fg r Fg D = 1 C ρ Av 2 2 r D Newton’s second law D − Fg = ma r Fg Begin to fall, acceleration, balance A effective cross-section area ρ air density The terminal speed: 1 2 C drag coefficient The Department of Physics, CUHK C ρ Av t2 − Fg = 0 vt = 2 Fg CρA The Department of Physics, CUHK 9 The drag force and terminal speed 10 Sample problem 5 Some terminal speed in air A raindrop with radius R=1.5mm falls from a cloud that is at height h=1200 m above the ground. The drag coefficient C for the drop is 0.60. Assuming that the drop is spherical throughout its fall. The density of water is 1000kg/m3, and the density of air is 1.2kg/m3. Object Terminal speed speed ( m/s) 95% distance distance (m) Sky diver 60 430 Baseball 42 210 Tennis ball 31 115 1. What is the terminal speed of the drop? Basketball 20 47 Ping-pong ball 9 10 2. What could be the drop’s speed just before impact if there is no drag force? Raindrop 7 6 The Department of Physics, CUHK The Department of Physics, CUHK 11 12 2 §5. Uniform circular motion Uniform circular motion Example 1: rounding a curve in a car When a body moves in a circle at constant speed, the centripetal acceleration is By the Newton’s second law, a force must cause the acceleration. The force from the right wall of the car jams you and provides you the needed centripetal force. 2 a= v R Your sensation: the compression on your body. where R is the radius of the circle. The Department of Physics, CUHK The Department of Physics, CUHK 13 Uniform circular motion 14 Uniform circular motion Example 2: orbiting Earth A centripetal force accelerates a body by changing the direction direction of the body ’s velocity without changing the body body’s speed. If you are a passenger in the shuttle. The gravitational force provides you the centripetal force. F =m v2 R Attention: the directions of the centripetal force and acceleration are not constant. Your sensation: weightlessness. The Department of Physics, CUHK The Department of Physics, CUHK 15 Sample problem 6 16 Sample problem Igor is a cosmonaut on the International Space Station, in a circular orbit around Earth, at an altitude h of 520 km and with a constant speed of 7.6km/s. Igor’s mass is 79 kg. Curved portions of highway are always banked (tilted) to prevent cars from sliding off the highway. When a highway is dry, the frictional force between the tires and the road surface may be enough to prevent sliding. When the highway is wet, however, the frictional force may be negligible and banking it then essential. 1. What is his acceleration? 2. What force does Earth exert on Igor? A car of mass m moves at a constant speed v of 20m/s around a banked circular track of radius R=190m. If the frictional force from the track is negligible, what bank angle θ prevents sliding. The The Department of Physics, CUHK The Department of Physics, CUHK 17 18 3 §6. Review & Summary Review & Summary Drag force: when there is a relative motion between air and a body, the body experiences a drag force. Friction: when a force tends to slide a body along a surface, a frictional force from the surface acts on the body. 1. 2. D = 1 C ρ Av 2 2 If the body does not move, then the static frictional force fs and the component of F which is parallel to the surface are equal in magnitude and opposite in direction. The magnitude of fs has a maximum f s , max = µ s FN 3. Terminal speed µ s coefficient of static friction 1 2 If the body begins to slide along the surface, the magnitude of fk is f k , max = µ k FN C ρ Av 2 − Fg = 0 t vt = 2 Fg C ρA µk coefficient of kenetic friction The Department of Physics, CUHK The Department of Physics, CUHK 19 20 Review & Summary Uniform circular motion: if a particle moves in a circle at constant speed, the particle is said to be in uniform circular motion. a= v2 R F =m v2 R The Department of Physics, CUHK 21 4...
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This document was uploaded on 09/16/2013.

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