Question

A force Fx=cx-3.00x2 acts on a virus as the virus moves along an x axis, with F measured in Newtons, x in meters, and c a constant. At x = 0, the virus’s kinetic energy is 20.0 J, while at x = 3.00 m, it is 11.0 J. Find c.

Answer 1

Answer:

4

Explanation:

We are given that

$F_x=cx-3x^2$

K.E at x=0 m=20 J

K.E at x=3 m=11 J

We have to find the value of c.

By work energy theorem

Work done=Change in kinetic energy

W=$\int_{0}^{3} Fdx=\int_{0}^{3}(cx-3x^2)dx$

$W=[\frac{cx^2}{2}-x^3]^{3}_{0}$

$W=\frac{9c}{2}-27$

$\Delta K=11-20=-9 J$

$-9=\frac{9c}{2}-27$

$-9+27=\frac{9c}{2}$

$18=\frac{9c}{2}$

$c=\frac{2}{9}\times 18=4$