Bukhovtsev-et-al-Problems-in-Elementary-Physics

MECHANICS
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33
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Fig. 49 Fig. 50
for the rocket to reach a maximum alti tude? The fuel burns
instantaneously. Disregard the resistance of the air.
129. The fuel in a rocket burns in equal portions with a
mass m. Combustion takes place instantaneously. Will the outftow
velocity of the gases be constant with respect to the rocket if
the mechanical energy of the system changes the same amount
upon the combustion of each portion?
130. A body is first lifted to the top of a mountain over the
path ADC, and again over the path ABC (Fig. 49). Prove that
the work done will be the same provided the body is lifted
slowly if the coefficient of friction is the same on both slopes.
13t. What force should be applied to the handle of a screw
jack to hold in equilibrium the load G lifted by the jack? The
pitch of the screw is h and the length of the handle is R. There
is no friction. ' '
132. Find the maximum efficiency of a screw jack having no
special device to prevent back travel.
133. A rope ladder with a length I carrying a man with a
mass m at its end is attached to the basket of a balloon with
a mass M. The entire system is in equilibrium in the air. Find
the work the man should do to climb into the basket. What is
the velocity of the balloon if the man climbs the ladder with a
velocity v with respect to it?
134. How should the power of a pump motor change for the
pump to deliver twice as much water in a unit of time through
a narrow orifice? Disregard friction.
135. A rectangular pit with an area at its base A and a depth
H is half filled with water. A pump forces the water up onto
the surface through a cylindrical pipe with a radius R.
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