A particle moves on the positive x axis (x > 0). A force F ( x ) = + k / x^2 pus

Question

A particle moves on the positive x axis (x > 0). A force F(x) = + k / x^2 pushes the particle to larger x. Note that the force decreases to 0 as x approaches infinity. Suppose the initial conditions at t = 0 arex(0) = x0and (dx/dt)0= 0. Solve for the motion of the particle.
(A) Calculate the velocity in the limit that t approaches infinity.
[Data: m = 0.37 kg; k = 1.52 Nm^2; x0= 1.8 m ]

(B) Calculate the time t when v is equal to 0.50 v(infinity).
[Hint: The position (x) and time (t) can be related by parametric equations
x = x0cosh^2 (theta)= (x0/2){ cosh2(theta)+ 1 }
and t = C { sinh2(theta) + 2(theta)}
where C is a constant, which you will need to determine.]

Explanation / Answer

part1)

Vlim needs to be found

a=F(x)/m;

Vdv/dx=F(x)/m;

now integrate

V^2/2=k/m(1/1.8-1/x);

as t=infinity so x=infinity

V^2/2=k/m(1/1.8)

so Vlim=2.136 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.