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Question Number 22139 by Tinkutara last updated on 11/Oct/17

$$\mathrm{The}\mathrm{linear}\mathrm{mass}\mathrm{density},i.e.\mathrm{mass}\mathrm{per}$$$$\mathrm{unit}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{rope},\mathrm{varies}\mathrm{from}0\mathrm{to}$$$$\lambda \mathrm{from}\mathrm{one}\mathrm{end}\mathrm{to}\mathrm{another}.\mathrm{The}$$$$\mathrm{acceleration}\mathrm{of}\mathrm{the}\mathrm{combined}\mathrm{system}$$$$\mathrm{will}\mathrm{be}$$

Commented by Tinkutara last updated on 11/Oct/17

Commented by ajfour last updated on 11/Oct/17

$$letmassofropebem.$$$$m=\int dm={\int }_0^L\mu dx={\int }_0^L\left(\frac{\lambda x}{L}\right)dx$$$$=\frac{\lambda x^2}{2L}{\mid }_0^L=\frac{\lambda L}{2}$$$$acceleration=\frac{F}{M+m}$$$$a=\frac{2F}{2M+\lambda L}.$$

Commented by Tinkutara last updated on 11/Oct/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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