Recent content by Trevorman

Homework Statement Derive from the formulas ##\frac{D^\pm}{Dt}(u \pm F) = 0## where ##\frac{D^\pm}{Dt} = \frac{\partial}{dt} + ( u \pm c) \frac{\partial}{\partial x}## the one-dimensional wave equation in the acoustical limit. \begin{cases} u << c\\ c \approx c0 = const\\ F =...

Okey so I have some additional information now. When a "stiff" mass hits a rod a exponentially decaying pressure-wave is formed. The pressure wave has a front with the size -zV. The wave propagates forward through the bar and when it is reflected at the free end it replace the signs and become...

"no matter how large the pushing force is" means that F is very large, this means that F >> mg, as a result ##mg+F*sin(\theta) \approx F*sin(\theta)##

Thank you for helping me Chet! I am familiar with the Wave equation but I cannot figure out how to setup the problem to get out the length of the piece, it is a tricky question. I will come back when I have more information of how the problem can be solved, been scratching my head over this for...

Hi, I have a Fourier problem that i do not know if it is valid to do the calculations like this. The Fourier transform looks like this ## \hat{v}(x,\omega) = \frac{\hat{F}(\omega)}{4(EI)^{\frac{1}{4}}i \omega^{\frac{3}{2}}(\rho A)^{\frac{3}{4}}}\left[ e^{-i\left[\omega^2 \frac{\rho A}{EI}...

##F_y=F*sin(\theta)## ##F_x=F*cos(\theta)## ##F_n-F_y = 0## Forces in y-direction Due to the constant velocity the forces in the x-direction ##F_x-F_k = 0## ##\theta## is the angle between F and ##F_x##. The result force diagram will look like the picture above, from there it is just geometry.

Sorry a miscalculation ## tan(\theta) = \frac{F_n}{F_k} = \frac{F*sin(\theta)}{F*cos(\theta)} = \frac{1}{\mu_k}## From this equation you can see that ##tan(\theta) = \frac{1}{\mu_k} \rightarrow \theta = tan^{-1}(\frac{1}{\mu_k})##

Well with that little info that you have, the ## F_k = \mu_k F_n ##, the friction force divided with the normal force ## \frac{F_k}{F_n} = \mu_k ##, means that the angle will become ##\theta = tan^{-1}(\mu_k)##. I can give you a more detailed explanation in a while.

What if you try to make a free body diagram, from that I get ## \mu_k ( F_{1} sin(\theta) + F_n) < F_1 cos(\theta) ## Where ##F_1## is the pushing force, ##F_n## the normal force of the box

One important aspect to overview is the impulse. You should try to have a dampening in the helmet so the force is spread out over time. From there you could look at different foams or other materials with low weight.

For those who have interest in this, I can give you the answer right away. Derivate the displacement with the boundary conditions, solve out all constants and you will get a very pretty expression that looks like this ## \hat{v}(x,\omega) = \frac{\hat{F}(\omega)}{4(EI)^{\frac{1}{4}}i...

The wave equation which is the simplest dynamic model for transverse motion of a beam is displayed below if it helps. ## v^{\prime \prime \prime \prime} + \frac{\rho A}{E I} \ddot{v} =0 ##

Hi thank you, this is my result from your suggestion. Is this correct? ## \sigma A - (\sigma + \Delta \sigma )A = A \Delta x \rho \frac{\partial^2 u}{\partial t^2}## ##-E\frac{\partial u}{\partial x}A =A\Delta x \rho \frac{\partial^2 u}{\partial t^2}## So the piece that is flying off...

1. A transversely directed transient force F(t) acts at the free end of a semi-infinite beam. a) Show how displacement, velocity, acceleration and strain at an arbitrary position along the beam can be determined. b) Calculate (MATLAB) the transversal acceleration (or an other quantity) at an...

Homework Statement Brittle materials as glass and ceramics have generally a much lower tensile strength than compressive strength. A rigid mass impacts the end of a bar (free-free) of such a material and a piece of the other end drops off. Is there a relation between the length of the piece...