Answer :
Answer:
Therefore,
The average power produced by friction as the rock stops is 156.86 Watts.
Explanation:
Given:
mass = m =20.0 kg
initial velocity,
[tex]v_{i}=8.00\ m/s[/tex]
coefficient of kinetic friction,
[tex]\mu_{k}=0.200\ m/s[/tex]
To Find:
average power, P =?
Solution:
According to Newton's Second Law,
[tex]Force=mass\times Acceleration[/tex]
Also Friction force,
[tex]Friction\ Force=-\mu_{k}mg[/tex]
Therefore,
[tex]Force=Friction\ Force[/tex]
Substituting the values we get
[tex]m\times a=-\mu_{k}mg\\\\a=-0.2\times 9.8=-1.96\ m/s^{2}[/tex]
Since Rock is getting stopped therefore acceleration is negative.
Final velocity will also be ZERO.
[tex]v_{f}=0\ m/s[/tex]
Now by Kinematic Equation
[tex]v_{f}=v_{i}+at[/tex]
Substituting the values we will get time 't',
[tex]t=-\dfrac{8}{-1.96}=4.08\ s[/tex]
Now according to work theorem ,
[tex]W=Change\ in\ Kinetic\ Energy[/tex]
which is equal to
[tex]W=\dfrac{1}{2}m((v_{f})^{2}-(v_{i})^{2})[/tex]
Substituting the values we get
[tex]W=-\dfrac{1}{2}\times 20\times 8^{2}=-640\ Joules[/tex]
Now ,
[tex]Power=|\dfrac{Work}{time}|[/tex]
Substituting the values we get
[tex]Power=|\dfrac{-640}{4.08}|=156.86\ Watt[/tex]
Therefore,
The average power produced by friction as the rock stops is 156.86 Watts.