8. A dart of mass m is accelerated horizontally through a tube of length L situated a heighth above the ground by a constant force F. Upon exiting the tube, the dart travels a horizontal distance Ax before striking the ground, as depicted in the diagram below. h ΔΧ (a) Develop an expression for the velocity of the dart, v, as it leaves the tube in terms of Ax, h, and any fundamental constants. (b) Derive an expression for the kinetic energy of the dart as it leaves the tube in terms of m, Ax, h, and any fundamental constants. (c) Derive an expression for the work done on the dart in the tube in terms of F and L. (d) Derive an expression for the height of the tube above the ground in terms of m, Ax, L, F, and fundamental any constants.
8. A dart of mass m is accelerated horizontally through a tube of length L situated a heighth above the ground by a constant force F. Upon exiting the tube, the dart travels a horizontal distance Ax before striking the ground, as depicted in the diagram below. h ΔΧ (a) Develop an expression for the velocity of the dart, v, as it leaves the tube in terms of Ax, h, and any fundamental constants. (b) Derive an expression for the kinetic energy of the dart as it leaves the tube in terms of m, Ax, h, and any fundamental constants. (c) Derive an expression for the work done on the dart in the tube in terms of F and L. (d) Derive an expression for the height of the tube above the ground in terms of m, Ax, L, F, and fundamental any constants.
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter2: Newtonian Mechanics-single Particle
Section: Chapter Questions
Problem 2.54P: A potato of mass 0.5 kg moves under Earth’s gravity with an air resistive force of −kmv. (a) Find...
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Can you please show a full derivation for Part D?
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