Complete Question
The complete question is shown on the first and second uploaded image
Answer:
The velocity is [tex]=4.51m/s[/tex]
Explanation:
The kinetic energy of the 9 kg can be determined by these expression
Kinetic energy of 9 kg block = initial energy stored - energy lost as a result of friction
Now to obtain the initial energy stored
Let U denote the initial energy stored and
[tex]U = \frac{1}{2} kx^2[/tex]
Where x is the length the spring is displaced
k is the force constant of the string
[tex]U = \frac{1}{2} * 627 * (0.6)^2[/tex]
[tex]= 112.86 J[/tex]
Now referring to the formula above
i.e Kinetic energy of 9 kg block = initial energy stored - energy lost as a result of friction
[tex]\frac{1}{2} mv^2 = 112.86 - \mu_kmgx[/tex]
[tex]v^2 = \frac{2(112.86 -\mu_kmgx)}{m}[/tex]
[tex]v = \sqrt{\frac{2(112,86- \mu_kmgx)}{m}}[/tex]
and we are told that coefficient of friction = 0.4 and the mass is 9 kg ,the acceleration due to gravity [tex]= 9.8m/s^2[/tex] this displacement length of spring = 0.6
Therefore [tex]v = \sqrt{\frac{2(112.86- (0.4 *9*9.8*0.6))}{9} }[/tex]
[tex]=4.51m/s[/tex]
