Problem Set 5 - 5.68 Maximum P and E of a Rocket The rocket...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5.68) Maximum P and E of a Rocket The rocket begins at rest with mass M , ejecting exhaust at speed u . We can use equation 5.54 to find the rocket’s current speed as a function of its remaining mass m ( t ) v ( t ) = u log M m ( t ) the rocket’s forward momentum is mv . If we subsitute in for velocity as a function of m , we see p = mu log M m Find when this is a maximum by taking the derivative with respect to m dp dm = u log M m- mu m M M m 2 = 0 → log M m = 1 So momentum is maximal when m = 1 e M Kinetic energy is given by 1 2 mv 2 = 1 2 mu 2 parenleftbigg log M m parenrightbigg 2 = 1 2 mu 2 parenleftBig log m M parenrightBig 2 Find the maximum by differentiating with respect to m ... 1 2 u 2 parenleftBig log m M parenrightBig 2 + mu 2 log parenleftBig m M parenrightBig 1 m = 0 → log parenleftBig m M parenrightBig =- 2 Which means m = 1 e 2 M 5.70) Snow on a Sled, Quantitative Sled begins with mass M and speed V , with snow accumulating on it at a rate σ . The essential fact in all three cases is that the momentum of the sled and the sled, along the direction of the track, is conserved. • If the snow is pushed off the sled, perpendicular to the tracks in the frame of the ground, then it will have no forward momentum, and the sled will have the same mass and momentum it had originally. Mv ( t ) = MV → v ( t ) = V • If nothing is done, we can determine from conservation of momentum that ( M + σt ) v ( t ) = MV → v ( t ) = M M + σt V 1 • If the snow is pushed off perpendicular to the sled’s tracks in the sled’s frame, its forward velocity will be the same as the sled’s (at the time the snow was pushed off) This means the sled will lose forward momentum at a rate proportional to its velocity times the rate snow is accumulating M dv dt =- σv → v ( t ) → dv dt =- σ M v which has solution v ( t ) =...
View Full Document

This note was uploaded on 01/22/2012 for the course PHYS 3201 taught by Professor Deheer during the Spring '10 term at Georgia Tech.

Page1 / 6

Problem Set 5 - 5.68 Maximum P and E of a Rocket The rocket...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online