The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?

In case of rocket, heat energy required for burning is at the cost kinetic energy of rocket.

Due to air friction the kinetic energy is converted into heat energy which burns up the rocket.
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An electron and a proton are detected in a cosmic ray experiment, the first with kinetic
energy 10 keV, and the second with 100 keV. Which is faster, the electron or the
proton ? Obtain the ratio of their speeds. (electron mass = 9.11×10-31 kg, proton mass
= 1.67×10–27 kg, 1 eV = 1.60 ×10–19 J).


Given that,

Kinetic energy,  

                           

K.E of proton,  

                         

K.E is given by, 

              

             
∴ ratio of their speed is given by,
                    

        = 13.54 

Thus electron is faster than proton by a magnitude of 13.54. 

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The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?



Let m be the mass of bob and l be the length of the string. If potent

Let m be the mass of bob and l be the length of the string. If potential energy of bob is taken zero at B, then potential energy of bob at A will be mgl. When bob reaches the point B, 5% of the potential energy is dissipated against air resistance, and rest of 95% is converted in kinetic energy.
∴                 1 half mv squared equals 0.95 mgl
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                           equals square root of 2 cross times 0.95 cross times 9.8 cross times 1.5 end root
                            equals 5.28 space straight m divided by straight s   
 
                            
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A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the trolley's floor at the rate of 0.05 kg m/s. What is the speed of the trolley after the entire sand bag is empty?

Sand leaks from the trolley with the same velocity which the trolley has initially.
Therefore, there is no change in momentum of sand and hence, the trolley.

Therefore, after the entire bag is emptied, the velocity of the trooley remains the same, i.e., 27 km/hr.
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A body of mass 2 kg initially at rest moves under the action of an applied horizontal forces of 7N on a table with co-efficient of kinetic friction 0.1. Compute:
(a) the work done by the applied force in 10 sec.,
(b) the work done by the friction force in 10 sec.,
(c) the work done by the net force on the body in 10 sec.,
(d) the change in kinetic energy of the body in 10 sec and interpret your results. 


It is given that
           m = 2 kg,                    F = 7N
          space straight mu equals 0.1,                      t = 10 sec

It is given that           m = 2 kg,                  
The force of friction between block and surface is,
                       f equals mu space m g space equals space 2 straight N
 The net accelerating force on body is,
                   F - f = 7 - 2 = 5N
∴     Acceleration,          a equals F over m equals 2.5 m divided by s squared
       Now the displacement undergone by the body in 10 sec is,
                           straight S equals ut plus 1 half at squared
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(a) Work done by applied force in 10 sec.,
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(b) Work done by friction force is,
     space space straight W subscript friction space equals space straight f times straight s space equals space 2 cross times 125 space equals space 250 space straight J
(c) Work done by net force is,
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(d) Change in kinetic energy of body is equal to the work done by net force = 625 J.




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