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1) A particle of mass m at rest is acted upon by a force F for a time t. Find its kinetic energy after an interval t. (answer should come

 \frac{ F^{2} t^{2} } {2m})

2) A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, what will be their respective kinetic energies in the ratio.
(answer should come 1:2)

3) Discuss whether any work is being done by each of the following agents and, if so, whether the work is positive or negative:
(a) a chicken scratching the ground (b) a person studying
(c) a crane lifting a bucket of concrete (d) the gravitational force on the bucket in part (c), (e) the leg muscles of a person in the act of sitting down.
(answer should come {a} Positive work {b} No work {c} negative work {d} positive work)



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Force F acts for time duration t.
Acceleration = F / m = a , 
as F is constant ,  a is constant.

v² - u² = 2 a s = 2 F / m * s
v² - 0 = 2 F s / m
1/2 m v² = F . s
   But  s = u t + 1/2 a t²    =  0 + 1/2 F/m * t²

KE = 1/2 m v² =  F * 1/2 F t²/m = F² t² / 2m
K.E. = 1/2 m v^2
  As K.E. is proportional to mass and velocities of bodies after falling 30 ft are both same for both masses,  the ratio is ratio of masses = 1 : 2.

OR, another way:
  K.E.  = 1/2 m (u^2 + 2 g h) = m g h, 
       h = height fallen,  g = acceleration due to gravity, m = mass

   KE1 / KE2 = m1 g h / m2 g h =  m1 / m2 = 1 : 2

a)  Work is done against friction force between ground and legs, and it is positive.

b)  person studying, if there is no movement, there is no work.  This is the picture in the bigger scene at high level.

     However, the reading activity involves, movement of eye muscles from left to right or right to left and top to bottom.  If more is to be read, there is work done in moving lips, moving neck from left to right.
       Hence there is work done by muscles against the friction force faced by muscles.

  When we read or see, images form on retina and these are taken to the brain through electrical voltage pulses (of magnitude milli volts).  So charge travels distance.  There is work done.  It is positive.

c)  a crane lifting - a bucket of concrete.
     The change in potential energy is the work done by the crane on the bucket of concrete.  There may not be change in KE of concrete between initial and final states.  But the position of concrete has changed in the Earth's gravitational field.

d) work done by the gravitational force on bucket of concrete = - change in the potential energy.  This is negative.  Gravity pulls an object down. In that case work is done by gravity and is positive.  Here the object has increased height. So  work is done against gravity and so it is negative work done by gravity.

e)  I dont know.  perhaps it is supposed to be zero ?

c , d  -- my answer is different from that you have given.

2 5 2
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