CHAPTER 8 HOMEWORK
1. (p.200 Ex.7) A particular spring obeys the force law F = (-kx + ax3 + bx4)i. (a) Is this force conservative? Explain why or why not. (b) If it is conservative, determine the form of the potential energy function.
2. (p.200 Ex.13) In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground in order to lift his center of mass 2.10m and cross the bar with a speed of 0.70m/s?
3. (p.201 Ex.21) A pendulum 2.00m long is released (from rest) at an angle qo = 30.0° (Fig. 8-15). Determine the speed of the 70.0-g bob (a) at the lowest point (q = 0); (b) at q = 15.0°; (c) at q = -15.0° (i.e., on the opposite side.) (d) Determine the tension in the cord at each of these three points. (e) If the bob is given an initial speed vo = 1.20m/s when released at q = 30.0°, recalculate the speeds for the parts (a), (b), and (c).
4. (p.201 Ex.29) A 90-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 350N. For the first 15m the floor is frictionless, and for the next 15m the coefficient of friction is 0.25. What is the final speed of the crate?
5. (p.202 Ex.39) determine the escape velocity from the Sun for an object (a) at the Sun's surface ( r = 7.0 x 105km, M = 2.0 x 1030kg). and (b) at the average distance of the Earth (1.50 x 108km). Compare to the speed of the Earth in its orbit.
6. (p.203 Ex.59) A driver notices that her 1000-kg car slows down from 90km/h to 70km/h in about 6.0s on the level when it is in neutral. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 80km/h?
*7. (p.201 Ex.24) A skier of mass m starts from rest at the top of a solid sphere of radius r and slides down its frictionless surface. (a) At what angle q (Fig. 8-31) will the skier leave the sphere? (b) If friction were present, would the skier fly off at a greater of lesser angle?
*8. (p.203 Ex.67) The position of a 280-g object is given (in meters) by x = 5.0t3 - 8.0t2 - 30t, where t is in seconds. Determine the net rate of work done on this object (a) at t = 2.0s and (b) at t = 4.0s. (c) What is the average net power input during the interval from t = 0s to t = 2.0s, and in the interval from t = 2.0s too 4.0s?