Computational Newton's second law problem

[Hobold]

Homework Statement

This is actually a very elementar Halliday's computational problem:

One person pushes a block with a force given by the equation $$F = 200e^{-0.15t}$$ (given in Newtons and seconds) and the block has, with the surface, a constant friction force of 80N. Find when the block stops moving and the distance moved.

Homework Equations

Newton's second law

The Attempt at a Solution

Considering Newton's second law, the problem seems to be obtaining the solution of the following differential equation:

$$200e^{-0.15t} - 80 = m \left( \frac{d^2x}{dt^2} \right)$$

This would actually be easy, though no mass is given. How can I solve numerically this equation not knowing the mass? Both Runge-Kutta and Euler's methods require it.

 

[gneill]

Under what conditions will the block keep moving?

 

[Hobold]

Velocity must not be null, though you can't solve for velocity if you don't have mass

 

[gneill]

Velocity must not be null,...

That's not quite what I intended to ask Rather than, "how can you tell that the block is moving", Under what conditions will the block continue to move? What is making the block move in the first place?

It may be that there is not enough information given for a particular numerical answer; you may have to make some assumptions for that. For example, no initial velocity is given. Will you assume that it is zero? No particular mass is specified. Will you provide an expression for an answer rather than a numerical value, or will you pick a mass value and get on with it...?

You should be able (I think) to determine expressions for the acceleration, velocity, and position. Given that you know all the forces involved, the acceleration is accessible...

...and it just may be that it turns out that the time when the velocity goes to zero is independent of the mass...

 

[SammyS]

If you assume that v₀ = 0, then the time it takes for the block to come to rest is independent of the mass.

To find the time, notice that d²x/dt² = dv/dt. Use this in your equation and integrate both sides w.r.t time, t. Then set v = 0 and solve for t (numerically or graphically).

The distance the block travels does depend on the mass.

 

[Hobold]

Thank you very much, I solved it, though there is no way you can solve for distance, right? I mean without assuming anything about mass.

 

[gneill]

Thank you very much, I solved it, though there is no way you can solve for distance, right? I mean without assuming anything about mass.

You can find an expression for the distance that depends upon mass.