6 - Circular Motion and Other Applications of Newton's Laws

Is not easy to determine the accuracy of an euler

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Unformatted text preview: ation could be the force of gravity, a force of friction, a force of string tension, or a normal force. A particle moving in nonuniform circular motion has both a centripetal component of acceleration and a nonzero tangential component of acceleration. In the case of a particle rotating in a vertical circle, the force of gravity provides the tangential component of acceleration and part or all of the centripetal component of acceleration. Be sure you understand the directions and magnitudes of the velocity and acceleration vectors for nonuniform circular motion. An observer in a noninertial (accelerating) frame of reference must introduce ﬁctitious forces when applying Newton’s second law in that frame. If these ﬁctitious forces are properly deﬁned, the description of motion in the noninertial frame is equivalent to that made by an observer in an inertial frame. However, the observers in the two frames do not agree on the causes of the motion. You should be able to distinguish between inertial and noninertial frames and identify the ﬁctitious forces acting in a noninertial frame. A body moving through a liquid or gas experiences a resistive force that is speed-dependent. This resistive force, which opposes the motion, generally increases with speed. The magnitude of the resistive force depends on the shape of the body and on the properties of the medium through which the body is moving. In the limiting case for a falling body, when the magnitude of the resistive force equals the body’s weight, the body reaches its terminal speed. You should be able to apply Newton’s laws to analyze the motion of objects moving under the inﬂuence of resistive forces. You may need to apply Euler’s method if the force depends on velocity, as it does for air drag. QUESTIONS 1. Because the Earth rotates about its axis and revolves around the Sun, it is a noninertial frame of reference. Assuming the Earth is a uniform sphere, why would the ap- parent weight of an object be greater at the poles than at the equator? 2. Explain why the Earth bulges at the equator. Problems 3. Why is it that an astronaut in a space capsule orbiting the Earth experiences a feeling of weightlessness? 4. Why does mud ﬂy off a rapidly turning automobile tire? 5. Imagine that you attach a heavy object to one end of a spring and then whirl the spring and object in a horizontal circle (by holding the free end of the spring). Does the spring stretch? If so, why? Discuss this in terms of the force causing the circular motion. 6. It has been suggested that rotating cylinders about 10 mi in length and 5 mi in diameter be placed in space and used as colonies. The purpose of the rotation is to simulate gravity for the inhabitants. Explain this concept for producing an effective gravity. 7. Why does a pilot tend to black out when pulling out of a steep dive? 173 8. Describe a situation in which a car driver can have a centripetal acceleration but no tangential acceleration. 9. Describe...
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This document was uploaded on 09/19/2013.

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