Suppose your mass is 70 kg. Suppose you\'re standing at rest on very slippery ic

Question

Suppose your mass is 70 kg. Suppose you're standing at rest on very slippery ice, so that friction
can be ignored.
• (a) If you were to be given a push by somebody so that you acquired 1 Joule of kinetic energy,
what would your momentum be and what would your speed be? (Remember, from some
earlier physics course, that the formula for kinetic energy of an object with mass m and speed v
is (1/2)mv2.)
• (b) Suppose that instead of being pushed, you acquired 1 Joule of energy by absorbing light that
was all coming from one direction. What would your momentum be, and what would your
speed be? (In this problem you need to apply conservation of momentum: you acquire the
photons' momentum when you absorb them.)
• (c) The answers to (a) and (b) for your speed should be very different. How is that consistent
with the principle of conservation of energy?

Explanation / Answer

a) 0.5*m*v^2 = K.E

=> V = sqrt(1*2/70) = 0.169 m/s Answer

So momentum = mv = 70*0.169 = 11.83 Kg*m/s Answer

b) average lambda of visible region = 565 nm

Energy = hc/lambda = 1240/565 = 2.1946 ev

So for 1 joule total photons are 1/(2.1946*1.6*10^-19) = 2.847*10^18 Photons

so momentum = h/lambda = 6.626*10^-34/(565*10^-9) = 1.172*10^-27 Kg*m/s

So total momentum = 2.847*(10^18)*1.172*(10^-27) = 3.336*10^-9 Kg*m/s

this much momentum is transfered to man So momentum = 3.336*10^-9 Kg*m/s Answer

and speed = 3.336*10^-9/70 = 4.7657*10^-11 m/s Answer

c) energy and momentum is conserved. most of energy will be convert into heat which man will feel not in kinetic energy of man.

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