MHB Challenging Classical Mechanics Problems: Can You Solve Them?

[johnherald]

Hello i have the difficulty in solving this two problems..thank you for your help math help boards :-) View attachment 8748

 

[skeeter]

1.6

distance up the incline (with kinetic friction present) ...

$\Delta x = \dfrac{v_f^2 - v_0^2}{2a}$

time up the incline ...

$t = \dfrac{v_f-v_0}{a}$

... where $v_f=0$ and $a = -g(\sin{\theta} + \mu \cos{\theta})$time down the incline ...

$\Delta x = v_0 \cdot t + \dfrac{1}{2}at^2 \implies t = \sqrt{\dfrac{2\Delta x}{a}}$

note $v_0 = 0$, $\Delta x$ is the opposite of that found going up the incline and $a = -g(\sin{\theta} - \mu \cos{\theta})$

 

[Dethrone]

1.5 is related to d'Alembert's principle. We can analyze the dynamics of an accelerating frame of reference (i.e non-inertial) by adding a fictitious force. Since the force in system A is $m*100$, then a fictitious force of $m*10$ must be added to system B so that the dynamics in both systems are equivalent.

 

[johnherald]

thanks a lot that will help me solving the other problems similar to that two particular question...:-)
and i have the difficulty solving some problems specially to the questions without a value.. thank you again for your help..