- #91
Karol
- 1,380
- 22
after ##\theta_0## the ball reaches the other side of the bowl, to ##\pi-\theta_0##:
$$\mu_{s}(\pi-\theta_0)=\frac{2\,cos(\pi-\theta_0)}{17\,sin(\pi-\theta_0)-10\,sin\theta_{0}+\frac{7R}{g}\omega_{0}^2}=\frac{-2\cos\theta_0}{7\sin\theta_0+\frac{7R}{g}\omega_0^2}<0$$
Also how do you know that for this particular problem, not in general: ##\mu_{s}^{(max)}\geq \mu_{k}##
We don't know ##\mu_k## and not ##\mu_s## simce we don't know ##\theta_0## and ##\omega_0##
$$\mu_{s}(\pi-\theta_0)=\frac{2\,cos(\pi-\theta_0)}{17\,sin(\pi-\theta_0)-10\,sin\theta_{0}+\frac{7R}{g}\omega_{0}^2}=\frac{-2\cos\theta_0}{7\sin\theta_0+\frac{7R}{g}\omega_0^2}<0$$
Also how do you know that for this particular problem, not in general: ##\mu_{s}^{(max)}\geq \mu_{k}##
We don't know ##\mu_k## and not ##\mu_s## simce we don't know ##\theta_0## and ##\omega_0##
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