Respuesta :
Specific Power S.P=0.49 W/kg
The power when an amount of energy ΔE is transferred in a time interval Δt is given by:
P= Δt/ΔE.........(1)
The gravitational potential energy of an object of mass m at height y (assuming [tex]U_g = 0[/tex] at y = 0) is given by:
[tex]U_g[/tex] = mgy.........(2)
The specific power of a person (or animal, machine, or device) of mass m doing the transformation or the work is given by:
specific power= mass of agent causing the transformation of transfer /power of a transformation or a transfer
The mass of the sloth is m= 4 kg and it climbs a height of h = 6 m in Δt=20 min 120 s.
Let its initial height be the zero gravitational potential energy level y=0; So its final height is yf = h
So, from equation (2), the change in the sloth's gravitational potential energy is:
ΔE=Uf−Ui =mg(h−0)=mgh
Now, we plug our values for m and h, so we get:
ΔE=(4.0 kg)×(9.8 m/[tex]s^2[/tex])×(6.0 m)
=235 J
Then, we plug our values for ΔE and Δt into equation (1), so we get the output power of the sloth:
P= 120 s/235 J
=1.96 W
Finally, we plug our values for P and m into equation (3), so we get the specific power of the sloth for this climb:
S.P= 4.0 kg/1.96 W
=0.49 W/kg
∴ S.P=0.49 W/kg
To know more about power here:
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