Let F be the magnitude of the frictional force. This force performs an amount of work W on the bullet such that
W = -Fx
where x is the distance over which F is acting. This is the only force acting on the bullet as it penetrates the tree. The work-energy theorem says the total work performed on a body is equal to the change in that body's kinetic energy, so we have
W = ∆K
-Fx = 0 - 1/2 mv²
where m is the body's mass and v is its speed.
Solve for F and plug in the given information:
F = mv²/(2x)
F = (0.00426 kg) (881 m/s)² / (2 (0.0444 m))
F = 37,234.8 N ≈ 37.2 kN
<span>Carnot cycle efficiency = work done/heat supplied = (Th - Tc)/Th
where, Th is temperature of hot reservoir and Tc is temperature of cold reservoir.
we have given the values as Heat supplied = 1.3 MJ or 1300 KJ, Th = 427 degree C and Tc = 90 degree C.
converting degree Celsius to kelvin temperatures, Th = 427 + 273 = 700 K
Tc = 90 +273 = 363
solving equations, (700 - 363)/700 = work done / 1300
work done = 625.86 KJ i.e. 0.626 MJ work is done .</span>
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