Respuesta :
The speed of the mass is [tex]\sqrt{0.9576}[/tex] m/s.
What is Kinetic energy?
- The energy that an object has as a result of motion is known as kinetic energy.
- It is described as the effort required to move a mass-determined body from rest to the indicated velocity.
- The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.
Calculation of speed of mass:
Assuming there is no air resistance or friction in this.
For this, energy conservation can be used. Gravitational potential energy does not change as height does, but spring potential energy does.
[tex]KE_i + SE_i = FE_f + SE_f[/tex]
Spring potential energy is SE, and kinetic energy is KE.
Since the mass is initially not moving, KE i = 0, and subsequently SE i is determined.
Let's plug everything in: 5kx, where k is the spring constant and x is the distance from the equilibrium point.
[tex]KE_i + SE_i = FE_f + SE_f[/tex]
[tex]0.5m(v_i) ^{2}[/tex]) + [tex]0.5k(x_i)^{2}[/tex] =[tex]0.5m(v_f)^{2}[/tex] + [tex]0.5k(x_f)^{2}[/tex]
[tex]0.5*0.3(0)^{2}[/tex] + [tex]0.5*26.6*(0.12)^{2}[/tex] = [tex]0.5*0.3(v_f)^{2}[/tex] + [tex]0.5*26.6*(.06)^{2}[/tex]
[tex]0.5*26.6(.12)^{2}[/tex] =[tex]0 .5*0.3(v_f)^{2}[/tex] + [tex]0 .5*26.6(.06)^{2}[/tex]
0.19152 = [tex]0.5*0.3(v_f)^{2}[/tex]+ 0.04788
0.14364 = [tex]0 .5*0.3(v_f)^{2}[/tex]
0.9576 = [tex](v_f)^{2}[/tex]
[tex]\sqrt{0.9576}[/tex] =[tex]v_f[/tex]
Hence the speed of the mass is [tex]\sqrt{0.9576}[/tex] m/s.
Learn more about Kinetic energy here:
https://brainly.com/question/999862
#SPJ4
