Answer:
3099 J
Explanation:
While the fireman slides down, his initial gravitational potential energy is converted partially into kinetic energy, partially into thermal energy, so we can write:
[tex]\Delta U = K + E_t[/tex] (1)
where
[tex]\Delta U [\tex] is the change in gravitational potential energy
K is the kinetic energy gained
Et is the thermal energy
The variation in gravitational potential energy is
[tex] U = mg \Delta h = (80 kg)(9.8 m/s^2)(4.2 m)=3293 J [/tex]
where m=80 kg is the mass of the fireman, g=9.8 m/s^2 is the acceleration of gravity, [tex]\Delta h=4.2 m[/tex] is the change in height of the fireman.
The kinetic energy gained is
[tex] K=\frac{1}{2}mv^2=\frac{1}{2}(80 kg)(2.2 m/s)^2=194 J[/tex]
where v = 2.2 m/s is the speed reached by the fireman at the bottom of the slide
So now solving eq.(1) we find the increase in thermal energy :
[tex] E_t = \Delta U - K = 3293 J - 194 J = 3099 J[/tex]
