VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
12th Edition
ISBN: 9781260265521
Author: BEER
Publisher: MCG
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Chapter 14.3, Problem 14.100P

A rocket weighs 2600 lb. including 2200 lb of fuel, which is consumed at the rate of 25 lb/s and ejected with a relative velocity of 13.000 ft/s. Knowing that the rocket is fired vertically from the ground, determine (a) its acceleration as it is fired, (b) its acceleration as the last particle of fuel is being consumed, (c) the altitude at which all the fuel has been consumed. (d) the velocity of the rocket at that time.

Expert Solution
Check Mark
To determine

The acceleration as it is fired of the rocket.

Answer to Problem 14.100P

The value of acceleration is a=92.8ft/s2

Explanation of Solution

The weight of the rocket as:

WR=mg

Substitute WR=2600Ibg=32.2ft/s2 we get

2600Ib=m(32.2ft/s2)m=260032.2=80.75Ib.s2/ft

Substitute required values, we get:

a=10.088×10380.7532.2ft/s2

=124.9332.2=92.8ft/s2

Expert Solution
Check Mark
To determine

The acceleration as the last particle of fuel is consumed.

Answer to Problem 14.100P

The value of acceleration as the last particle of fuel is a=780ft/s2.

Explanation of Solution

Find the weight of the rocket the condition is fuel is consumed.

Wo=WRWF

Substituting all required values, we get:

Wo=2600Ib2200Ib=400Ib

The weight of the rocket is:

Wo=mg400Ib=m(32.2)m=40032.2m=12.422Ib.s2/ft

Substitute all the values, we get:

a=Pmga=10.088×103Ib12.422Ib.s2/ft32.2ft/s2=812.232.2=779.9ft/s2=780ft/s2

Expert Solution
Check Mark
To determine

The altitude at which all the fuel has been consumed.

Answer to Problem 14.100P

The value of altitude at which all the fuel has been consumed is h=119.3mi.

Explanation of Solution

Formulate the relation for final velocity of the rocket is:

v=uln(momo(qt))gtdydt=uln(momo(qt))gt(1)dy=[uln(momo(qt))gt]dt

Consider the relation for the altitude of the rocket:

h=dy

Here dy=[uln(momo(qt))gt]dt

h=0t([uln(momo(qt))gt]dt)=u0tlnmoqtmodt12gt2(2)

Here z=moqtmo

So,

dz=qmodtdt=moqdz

Substitute these values, we get:

h=u0tlnz(moqdz)12gt2=mouqlnzdz12gt2=mouq[(zlnzz)]zoz12gt2

Substitute z=moqtmo in equation 2, we get:

h=mouq[moqtmo(lnmoqtmo1)momo(lnmomo1)]12gt2=mouq[(1qmot)×lnmoqtmo(1qmot)momo(lnmomo1)]12gt2

=mouq[lnmoqtmo(qmot×lnmoqtmo)+qmot]12gt2=(mouq×lnmoqtmo)(mouq×qmot×lnmoqtmo)+(mouq×qmot)12gt2

=(mouq×lnmoqtmo)(ut×lnmoqtmo)+(ut)12gt2(3)

Find the time t by using below formula, we get:

t=Wfqt=220025=88s

Substitute all the values, we get:

h=ut+(mouqut)lnmoqtmo12gt2=(13000×88)+[(2600×1300025(13000×88))ln260022002600]12(32.2)(88)2=1144000389334.85124678.4=629986.75ft×1mile5280fth=119.3mi

Expert Solution
Check Mark
To determine

The velocity of the rocket.

Answer to Problem 14.100P

The value of velocity at that time is V=14660mi/h.

Explanation of Solution

Substitute all the required values in equation 1, we get:

v=13000ln(260026002200)(32.2)(88)=21500ft/s×1mile5280ft×3600s1hr=14660mi/h

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Chapter 14 Solutions

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS

Ch. 14.1 - A system consists of three identical 19.32-lb...Ch. 14.1 - A system consists of three identical 19.32-lb...Ch. 14.1 - A system consists of three particles A, B, and C....Ch. 14.1 - For the system of particles of Prob. 14.13,...Ch. 14.1 - A 13-kg projectile is passing through the origin O...Ch. 14.1 - A 300-kg space vehicle traveling with a velocity...Ch. 14.1 - A 2-kg model rocket is launched vertically and...Ch. 14.1 - An 18-kg cannonball and a 12-kg cannonball are...Ch. 14.1 - Prob. 14.19PCh. 14.1 - Prob. 14.20PCh. 14.1 - An expert archer demonstrates his ability by...Ch. 14.1 - Two spheres, each of mass m, can slide freely on a...Ch. 14.1 - Prob. 14.23PCh. 14.1 - A 6-kg shell moving with a velocity...Ch. 14.1 - A 6-kg shell moving with a velocity...Ch. 14.1 - In a scattering experiment, an alpha particle A is...Ch. 14.1 - Derive the relation Ho=rmv+HG between the angular...Ch. 14.1 - Show that Eq. (14.23) may be derived directly from...Ch. 14.1 - Consider the frame of reference Ax'y'z' in...Ch. 14.1 - Show that the relation MA=HA where HA is defined...Ch. 14.2 - Determine the energy lost due to friction and the...Ch. 14.2 - Prob. 14.32PCh. 14.2 - In Prob. 14.6. determine the work done by the...Ch. 14.2 - Determine the energy lost as a result of the...Ch. 14.2 - Two automobiles A and B, of mass mA and mB,...Ch. 14.2 - It is assumed that each of the two automobiles...Ch. 14.2 - Solve Sample Prob. 14.5, assuming that cart A is...Ch. 14.2 - Ball B is suspended from a cord of length l...Ch. 14.2 - A 15-lb block B starts from rest and slides on the...Ch. 14.2 - A 40-lb block B is suspended from a 6-ft cord...Ch. 14.2 - In a game of pool, ball A is moving with a...Ch. 14.2 - In a game of pool, ball A is moving with a...Ch. 14.2 - Three spheres, each with a mass of m, can slide...Ch. 14.2 - In a game of pool, ball A is moving with the...Ch. 14.2 - The 2-kg sub-satellite B has an initial velocity...Ch. 14.2 - A 900-lb space vehicle traveling with a velocity...Ch. 14.2 - Four small disks A, B, C, and D can slide freely...Ch. 14.2 - In the scattering experiment of Prob. 14.26, it is...Ch. 14.2 - Prob. 14.49PCh. 14.2 - Three small spheres A, B, C, each of mass m, are...Ch. 14.2 - In a game of billiards, ball A is given an initial...Ch. 14.2 - For the game of billiards of Prob. 14.51, it is...Ch. 14.2 - Two small disks A and B of mass 3 kg and 1.5 kg,...Ch. 14.2 - Two small disks A and B of mass 2 kg and 1 kg,...Ch. 14.2 - Prob. 14.55PCh. 14.2 - Prob. 14.56PCh. 14.3 - A stream of water with a density of =1000kg/m3 is...Ch. 14.3 - A jet ski is placed in a channel and is tethered...Ch. 14.3 - Tree limbs and branches are being fed at A at the...Ch. 14.3 - The nozzle shown discharges water at the rate of...Ch. 14.3 - A rotary power plow is used to remove snow from a...Ch. 14.3 - A hose discharges water at a rate of 8 m3/min with...Ch. 14.3 - Sand falls from three hoppers onto a conveyor belt...Ch. 14.3 - The stream of water shown flows at a rate of 550...Ch. 14.3 - The nozzle shown discharges water at the rate of...Ch. 14.3 - A stream of water flowing at a rate of 1.2 m/min...Ch. 14.3 - A stream of water flowing at a rate of 1.2 m3/min...Ch. 14.3 - Prob. 14.68PCh. 14.3 - The total drag due to air friction on a jet...Ch. 14.3 - Prob. 14.70PCh. 14.3 - In order to shorten the distance required for...Ch. 14.3 - The helicopter shown can produce a maximum...Ch. 14.3 - Prior to takeoff, the pilot of a 3000-kg...Ch. 14.3 - The jet engine shown scoops in air at A at a rate...Ch. 14.3 - A jet airliner is cruising at a speed of 900 km/h...Ch. 14.3 - A 16-Mg jet airplane maintains a constant speed of...Ch. 14.3 - The propeller of a small airplane has a...Ch. 14.3 - The wind turbine generator shown has an...Ch. 14.3 - A wind turbine generator system having a diameter...Ch. 14.3 - While cruising in level flight at a speed of 570...Ch. 14.3 - In a Pelton-wheel turbine, a stream of water is...Ch. 14.3 - A circular reentrant orifice (also called Borda’s...Ch. 14.3 - A railroad car with length L and mass mg when...Ch. 14.3 - The depth of water flowing in a rectangular...Ch. 14.3 - Determine the rate of flow in the channel of Prob....Ch. 14.3 - A chain of length I and mass m lies in a pile on...Ch. 14.3 - Solve Prob. 14.86, assuming that the chain is...Ch. 14.3 - The ends of a chain lie in piles at A and C. When...Ch. 14.3 - A toy car is propelled by water that squirts from...Ch. 14.3 - A toy car is propelled by water that squirts from...Ch. 14.3 - The main propulsion system of a new space...Ch. 14.3 - The main propulsion system of a new space...Ch. 14.3 - A rocket sled bums fuel at the constant rate of...Ch. 14.3 - A space vehicle describing a circular orbit about...Ch. 14.3 - A 540-kg spacecraft is mounted on top of a rocket...Ch. 14.3 - The rocket used to launch the 540-kg spacecraft of...Ch. 14.3 - The weight of a spacecraft, including fuel, is...Ch. 14.3 - The rocket engines of a spacecraft are fired to...Ch. 14.3 - Determine the distance traveled by the spacecraft...Ch. 14.3 - A rocket weighs 2600 lb. including 2200 lb of...Ch. 14.3 - Determine the altitude reached by the spacecraft...Ch. 14.3 - For the spacecraft and the two-stage launching...Ch. 14.3 - In a jet airplane, the kinetic energy imparted to...Ch. 14.3 - In a rocket, the kinetic energy imparted to the...Ch. 14 - Three identical cars are being unloaded from an...Ch. 14 - A 50-kg mother and her 26-kg son are sledding down...Ch. 14 - An 80-Mg railroad engine A coasting at 6.5 km/h...Ch. 14 - In a game of pool, ball A is moving with a...Ch. 14 - Mass C, which has a mass of 4 kg, is suspended...Ch. 14 - A 15-lb block B is at rest and a spring of...Ch. 14 - A 6000-kg dump truck has a 1500-kg stone block...Ch. 14 - For the ceiling-mounted fan shown, determine the...Ch. 14 - An airplane with a weight W and a total wing span...Ch. 14 - The final component of a conveyor system receives...Ch. 14 - A garden sprinkler has four rotating arms, each of...Ch. 14 - A chain of length I and mass m falls through a...
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