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u4905047
neutrino

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 « on: September 13, 2007, 09:17:32 PM »

9.5 Figure 9.13 shows two blocks of masses and that slide on smooth planes inclined at angles and to the horizontal.The blocks are connected by a light inextensible string that passes over a light frictionaless pulley. Find the acceleration of the block of mass up the plane, and deduce the tension in the string.

Sol-n Let the system consists of two blocks of mass and .
Initially,The system is at rest.
At time , two blocks have
i)the same distance ( which is parallel to the incline)
ii)the same velocity
iii)the same acceleration
because they are fixed with the same string,and this string is light and inextensible.Thus tension is constant.

1.Find the acceleration of mass

Method 1 Newton 's law of motion

From the newton 's second law (in the direction which is parallel to the incline) of mass

;                                  =                            ........(1)

;                                  =                            ........(2)

(1)+(2);                        =

=

Method 2 Energy conservation
From energy conservation principle which can simplify as

the decreasing of potential energy       =         the increasing of kinetic energy.

=

=

=

=

differentiate with respect to t all the equation,and use and .then

=

=

=

and divided by ,thus

=

2.Find the tension .
From the newton 's second law of mass .

=

=

substitute then

=

=

=

7.19 A spacecraft travelling with speed V approaches a planet of mass M along straight lin whos perpendicular distance from the center of the planet is p. When the spacecraft is at a distance c from the planet, it fires its engines so as to multiply its current speed by a factor k( 0 < k < 1 ), its direction of motion being unaffected. [ You may neglect the time taken for this operation.] Find the condition that the spacecraft should go into orbit around the planet.

=

\frac{\partial N}{\partial x}
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