Problem Set 2 & Solutions - Phys116 Problem Set 2 Due:...

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Unformatted text preview: Phys116 Problem Set 2 Due: Friday, Sept. 12, 2003 before the start of class. Please write your TA's name at the top of your solution set. Communicate your reasoning in your solutions, concisely and clearly. Efforts are as important as correct answers. 1. While campaigning in California, imagine that Arnold Schwarzenegger finds himself on one cliff, separated by a chasm from a crowd of eager voters near a neighboring cliff. He wishes to jump over the chasm in a car. Here is a sketch of the situation: h L What is the minimum (horizontal) velocity required in order for the car to complete the jump successfully? You should approximate the car as a point object to keep things simple. Please do not try this at home. 2. A 40-kg girl and an 10-kg sled are on the surface of a frozen lake, 15 m apart. By means of a rope the girl exerts a 5-N (N stands for Newton) force on the sled, pulling it towards her. Assume that the frictional forces with the ice are negligible. (a) What is the acceleration of the sled? (b) What is the acceleration of the girl? (c) How far from the girl's initial position do they meet, presuming the force to remain constant? 3. An Olympic hammer thrower twirls around holding a ball on a chain while rotating in a fixed spot, and then lets go to hurl the ball as far as he can get it to go. Assume that there is a fixed force that the thrower is capable of exerting on the chain, independent of its properties, and that the mass M of the hammer is entirely in the ball, with negligible mass in the chain. Assume also that the ball moves in a circle, and ignore gravity. (You will also use that F=Ma.) (a) How will the ball's speed when the hammer is released depend on the rotation radius of the hammer R, for fixed M? (b) How will the ball's speed when the hammer is released depend on M, for fixed R? (c) How does the period T of rotation for the hammer thrower depend on R, M, and the force that he can exert? (d) Rules in hammer-throw competitions specify the allowable values of the mass M and the chain length. However if you wanted to change the rules to allow longer throws, what changes could you implement? 4. On a horizontal turntable that is rotating at constant angular speed there is a bug crawling outward on a radial line of the turntable such that the bug's distance from the center increases linearly with time. That is, r=bt, q=wt, where b and w are constants. (It is easiest to do this problem entirely in radial coordinates.) (a) Write an expression for the bug's position vector in polar notation. (b) Find an expression for the velocity of the bug as a function of time. (c) Find the bug's speed as a function of time. (d) Find an expression for the bug's acceleration as a function of time. (e) Find an expression for the angle between the bug's position vector and velocity as a function of time. 5. K&K, 2.3. 6. K&K, 2.4. If the particles are undergoing uniform circular motion about each other, you can also say that they are both undergoing uniform circular motion about some fixed point in between the particles, but possibly with different values of the radius for each particle. 7. Consider the rotation of the earth, but ignore its other motions in the universe. Objects sitting on the surface of the earth must experience an acceleration because they move in a circle as the earth rotates. (a) Find the magnitude and direction of this acceleration of an object sitting on the earth's surface, both at the equator and at Ithaca (approximately 42.4 degrees north of the equator). You can use that the earth's radius is approximately 6.4 106 m. Are these acceleration values large or small compared to the acceleration on a falling object due to gravity, g=9.8 m/s2 ? (b) Does the acceleration associated with rotation cause any change to the effective gravitational force that you feel? In other words, as measured by a scale do you weigh more or less on the spinning earth than you would on an earth that did not spin? (Even by a little bit?) For simplicity, consider only the case of a person on the equator. Explain your reasoning. (Hint: What would happen if the earth rotated very, very fast?) 8. K&K 1.21 (Challenging, but gives a simple interesting result. Liberal use of trig identities can simplify the algebra. Try eventually to reach an answer containing only angles, without any trigonometric functions like sines, cosines, or tangents.) p ^ 1 Useful trig fact: = tan - a ~ . tan a 2 ...
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This homework help was uploaded on 10/25/2007 for the course PHYS 1116 taught by Professor Elser, v during the Fall '05 term at Cornell University (Engineering School).

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