Respuesta :
We will use two definitions to solve this problem. The first will be given by the conservation of energy, whereby the change in kinetic energy must be equivalent to work. At the same time, work can be defined as the product between the force by the distance traveled. By matching these two expressions and clearing for the Force we can find the desired variable.
[tex]W = KE_f-KE_i[/tex]
[tex]Fd = \frac{1}{2}mv_f^2-\frac{1}{2} mv_i^2[/tex]
Thus the force acting on the sled is,
[tex]F = \frac{m}{2s} (v_f^2-v_i^2)[/tex]
Replacing,
[tex]F = \frac{8}{2(2.5)}(6^2-4^2)[/tex]
[tex]F = 32N[/tex]
Therefore the Force acting on the sled is 32N
The force acting on the sled is 6.4 N.
Work-energy theorem:
Given that the force (F) acting on the sled is constant and in the same direction of motion or displacement. So the work done by this force is:
W = Fd
where d is the distance traveled.
According to the work-energy theorem, the work done by a conservative or constant force is equal to the change in kinetic energy (ΔKE) of the system. That is:
W = ΔKE
Now, [tex]\Delta KE=\frac{1}{2} m(\Delta v)^2\\\\\Delta KE=\frac{1}{2}\times8\times(6-4)^2\\\\\Delta KE =16 \;J[/tex]
So, we get:
[tex]Fd = 16\;J\\\\F\times2.5=16\;J\\\\F=6.4\;N[/tex]
Learn more about work-energy theorem:
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