Respuesta :
Answer:
(a). The kinetic energy is 5.33 J
(b). The maximum kinetic energy is 5.33 J.
Explanation:
Given that,
Mass of block = 1.5 kg
Suppose the force is
[tex]F=(4-x^2)i\ N[/tex]
(a). We need to calculate the kinetic energy of the block
Using work energy theorem
[tex]\Delta k=W_{f}[/tex]
[tex]K(x)=\int_{0}^{x}{4-x^2}dx[/tex]
[tex]K(x)=4x-\dfrac{x^3}{3}[/tex]....(I)
Now put the value of x in equation
[tex]K(x)=4\times2-\dfrac{2^3}{3}[/tex]
[tex]K(x)=5.33\ J[/tex]
The kinetic energy is 5.33 J
For K to be minimum
[tex]\dfrac{dK}{dx}=0[/tex]
[tex]4-\dfrac{3x^2}{3}=0[/tex]
[tex]4-x^2=0[/tex]
[tex]x=2[/tex]
(b). We need to calculate the maximum kinetic energy of the block
For K to be maximum
[tex]\dfrac{d^2K}{dx^2}=0[/tex]
[tex]\dfrac{d^2K}{dx^2}=0-2x[/tex]
Put the value of x
[tex]\dfrac{d^2K}{dx^2}=-4[/tex]
Now put the value of x in equation (I)
[tex]K(x)=4\times2-\dfrac{2^3}{3}[/tex]
[tex]K(x)=5.33\ J[/tex]
The maximum kinetic energy is 5.33 J
Hence, (a). The kinetic energy is 5.33 J
(b). The maximum kinetic energy is 5.33 J.
