Respuesta :
We can use the law of conservation of energy to solve the problem.
At the top of the slide, Justin is still, so its velocity and its kinetic energy are zero. He only has gravitational potential energy U, so its total mechanical energy is:
[tex]E_i = U = mgh = (50 m)(9.81 m/s^2)(8.0m)=3924 J[/tex]
At the bottom of the slide, the height is now zero, so there is no potential energy left. Instead, Justin acquired a speed v, so its kinetic energy K will be different from zero now, and it will be:
[tex]E_f = K = \frac{1}{2}mv^2= \frac{1}{2}(50kg)(12 m/s)^2=3600 J [/tex]
So, the energy lost by Justin when going from top to bottom is
[tex]\Delta E = E_i-E_f = 3924 J-3600 J=324 J[/tex]
And since energy cannot be destroyed, this energy must have converted into something else, and in fact it corresponds to the thermal energy created by the frictional force during the descent.
At the top of the slide, Justin is still, so its velocity and its kinetic energy are zero. He only has gravitational potential energy U, so its total mechanical energy is:
[tex]E_i = U = mgh = (50 m)(9.81 m/s^2)(8.0m)=3924 J[/tex]
At the bottom of the slide, the height is now zero, so there is no potential energy left. Instead, Justin acquired a speed v, so its kinetic energy K will be different from zero now, and it will be:
[tex]E_f = K = \frac{1}{2}mv^2= \frac{1}{2}(50kg)(12 m/s)^2=3600 J [/tex]
So, the energy lost by Justin when going from top to bottom is
[tex]\Delta E = E_i-E_f = 3924 J-3600 J=324 J[/tex]
And since energy cannot be destroyed, this energy must have converted into something else, and in fact it corresponds to the thermal energy created by the frictional force during the descent.
The converted energy of [tex]324\;J[/tex] is the thermal energy created by the friction during his descent.
Explanation:
Given information:
Mass of justin [tex]=50 \; \text{kg}[/tex]
Height of water slide [tex]=8\;\text{m}[/tex]
Speed at the bottom [tex]= 12 \;\text{m/s}[/tex]
Now, the total mechanical energy is:
[tex]E_i=U=mgh\\E_i=50\times 9.81\times 8\\E_i=3924\;J[/tex]
And, the kinetic energy :
[tex]E_f=K=(1/2)mv^2\\E_f=0.50\times 50\times 12\\E_f=3600\;\text{J}[/tex]
So, the energy lost by the justin:
[tex]\Delta\;E=E_i-E_f\\\Delta\;E=3924-3600\\\Delta\;E=324J\\[/tex]
Hence, this converted energy of [tex]324\;J[/tex] is the thermal energy created by the friction during his descent.
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