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23 Nov 2019
A particle moves on the positive x axis (x > 0). A force F(x) =+ k / x2 pushes the particle to larger x. Note that the forcedecreases to 0 as x approaches infinity.
Suppose the initial conditions at t = 0 are x(0) = x0 and (dx/dt)0= 0.
Solve for the motion of the particle.
(A) Calculate the time t when v is equal to 0.50 v(infinity).
[Hint:
The position (x) and time (t) can be related by parametricequations
x = x0 cosh2? = (x0/2){ cosh2?+ 1 }
and t = C { sinh2? + 2?}
where C is a constant, which you will need to determine.]
A particle moves on the positive x axis (x > 0). A force F(x) =+ k / x2 pushes the particle to larger x. Note that the forcedecreases to 0 as x approaches infinity.
Suppose the initial conditions at t = 0 are x(0) = x0 and (dx/dt)0= 0.
Solve for the motion of the particle.
(A) Calculate the time t when v is equal to 0.50 v(infinity).
[Hint:
The position (x) and time (t) can be related by parametricequations
x = x0 cosh2? = (x0/2){ cosh2?+ 1 }
and t = C { sinh2? + 2?}
where C is a constant, which you will need to determine.]
Jean KeelingLv2
7 Mar 2019
