Question

A body with a mass of 7.41 kg moves along the x ‑axis, influenced by a conservative force F ( x ) . → F ( x ) = A x 3 ^ x where A = − 4 N m 3 When the body is at position x i = 2.05 m, it is moving with a speed of v i = 6.51 m / s. What is the body's speed when it is at position x f = − 2.65 m?

Answer 1

Answer:

7.136 m/s

Explanation:

We are given that

Mass =m=7.41 kg

$F(x)=Ax^3 hat{x}$

Where $A=-4 N/m^3$

$x_i=2.05 m$

$u=v_i=6.51 m/s$

We have to find the speed of body when it is position $x_f=-2.65 m$

According to work energy theorem

[tex[K_f-K_i=Work\; done[/tex]

$\frac{1}{2}mv^2-\frac{1}{2}mu^2=\int_{2.05}^{-2.65}-4x^3 dx$

$\frac{1}{2}m(v^2-u^2)=-[x^4]^{2.05}_{-2.65}$

$\frac{1}{2}(7.41)(v^2-(6.51)^2)=-((2.05)^4-(2.65)^2)$

$\frac{1}{2}(7.41)(v^2-42.3801)=31.6545$

$v^2-42.3801=\frac{31.6545\times 2}{7.41}$

$v^2-42.3801=8.5437$

$v^2=8.5437+42.3801=$

$v=\sqrt{8.5437+42.3801}$

$v=7.136 m/s$