Horizons: Exploring the Universe - With MindTap
Horizons: Exploring the Universe - With MindTap
14th Edition
ISBN: 9781337578080
Author: Seeds
Publisher: Cengage
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Chapter 16, Problem 1LTL
To determine

The reason for the production of volcanoes scattered over the Pacific Ocean.

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8.114 CALC A Variable-Mass Raindrop. In a rocket-propul- sion problem the mass is variable. Another such problem is a rain- drop falling through a cloud of small water droplets. Some of these small droplets adhere to the raindrop, thereby increasing its mass as it falls. The force on the raindrop is dp dv dm Fext = + dt dt dt = Suppose the mass of the raindrop depends on the distance x that it has fallen. Then m kx, where k is a constant, and dm/dt = kv. This gives, since Fext = mg, dv mg = m + v(kv) dt Or, dividing by k, dv xgx + v² dt This is a differential equation that has a solution of the form v = at, where a is the acceleration and is constant. Take the initial velocity of the raindrop to be zero. (a) Using the proposed solution for v, find the acceleration a. (b) Find the distance the raindrop has fallen in t = 3.00 s. (c) Given that k = 2.00 g/m, find the mass of the raindrop at t = 3.00 s. (For many more intriguing aspects of this problem, see K. S. Krane, American Journal of…
8.13 A 2.00-kg stone is sliding Figure E8.13 F (kN) to the right on a frictionless hori- zontal surface at 5.00 m/s when it is suddenly struck by an object that exerts a large horizontal force on it for a short period of 2.50 time. The graph in Fig. E8.13 shows the magnitude of this force as a function of time. (a) What impulse does this force exert on t (ms) 15.0 16.0 the stone? (b) Just after the force stops acting, find the magnitude and direction of the stone's velocity if the force acts (i) to the right or (ii) to the left.
Please calculate the expectation value for E and the uncertainty in E for this wavefunction trapped in a simple harmonic oscillator potential
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