Respuesta :
Answer:
The work done by the non-conservative force is 491.43 J
Explanation:
You have to apply the Work-Energy Theorem for mechanical energy, which is:
W non-conservative force = ΔEm
Where ΔEm is the variation of mechanical energy between two points of the movement.
ΔEm= Emf-Emi
Emf: Final mechanical energy
Emi: Initial mechanical energy
Also, the mechanical energy is:
Em= Ep+Ek
Where Ep is the potential energy and Ek is the kinetic energy.
In this case, the potential energy is gravitational, due to the change in the height.
Ep= mgh (m is the mass, g the acceleration of gravity and h is the height)
Ek= 0.5mv² (m is the mass, v is the speed)
Wncf = Epf+Ekf - (Epi+Eki)
The initial mechanical energy is:
Emi= mgh + 0.5mvi²
Replacing the values of m, g, h and vi:
Emi= (41.4)(9.8)(2.91) + 0.5(41.4)(1.22)²
Emi=1211.45 J
The final mechanical energy is:
Emf = Ekf
There isn't potential energy because at the bottom of the wave the height is zero.
Emf= 0.5mvf²
Replacing m=41.4 kg and vf=9.07 m/s
Emf = 0.5(41.4)(9.07)²
Emf=1702.88 J
Therefore:
Wncf = 1702.88 - 1211.45 = 491.43 J
The work done by the (non-conservative) force of the wave is equal to 491.43 Joules.
Given the following data:
Initial velocity = 1.22 m/s.
Final speed = 9.07 m/s.
Height = 2.91 m.
Mass = 41.4 kg.
How to calculate work done.
In Science, work done is generally calculated by multiplying force and the vertical height or displacement experienced by an object.
Mathematically, the work done by the (non-conservative) force of the wave is given by this formula:
[tex]W=E_f-E_i\\\\W=\frac{1}{2}mv_i^2-(mgh+\frac{1}{2}mv_i^2) \\\\[/tex]
Substituting the given parameters into the formula, we have;
[tex]W=\frac{1}{2}\times 41.4 \times 1.22^2-(41.4 \times 9.8 \times 2.91+\frac{1}{2}\times 41.4 \times 9.07^2)\\\\W=1702.88-1211.45[/tex]
W = 491.43 Joules.
Read more on work done here: brainly.com/question/22599382
