Chapter 3: Motion in 2 or 3 Dimensions. Position & Velocity Vectors. Position Vector. To describe the motion of a particle in space, we first need to describe the position of the particle.
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A cow is launched from the top of a hill with an initial velocity vector that makes an angle of 45 degrees with the horizontal. The projectile lands at a point that is 10 m vertically below the launch point and 300 m horizontally away from the launch point.
A particle that is undergoing motion in such a manner that its direction is changing is experiencing a radial acceleration that has magnitude equal to the square of its velocity divided by the instantaneous radius of curvature of its motion. The direction of this radial, or centripetal, acceleration is toward the center of circular path of particle's motion.
A car has a “lateral acceleration” of 0.87g, which is (0.87)/(9.8m/s2)=8.5m/s2. This represents the maximum centripetal acceleration that can be attained without skidding out of the circular path. If the car is traveling at a constant speed 40m/s (~89mi/h, or 144km/h), what is the max radius of curve it can negotiate?
IDENTIFY and SET UP
Car travels along a curve, speed is constant apply equation of circular motion to find the target variable R.
An object that is undergoing non-uniform circular motion, or motion where the magnitude and the direction of the velocity is changing, will experience an acceleration that can be described by two components:
A radial or centripetal acceleration equal to the square of speed divided by radius of curvature of motion directed toward the center of curvature of the motion, and
Tangential component of acceleration that is equal to the rate of change of the particle's speed and is directed either parallel (in the case of speeding up) or anti-parallel (in the case of slowing down) to the particle's velocity.