Slope and pulley problem ? Please guide me. Thank you in advance

One of two identical masses lies on a smooth plane, which is inclined at sin-1 1/14 to the horizontal, and is 2m from the top. A light inextensible string attached to this mass passes along the line of greatest slope , over a smooth pulley fixed at the top of the incline; the other end carries to the other mass hanging freely 1m above the floor. If the system is released from rest, find the time taken for the hanging mass to reach the floor?

Re: Slope and pulley problem ? Please guide me. Thank you in advance

You question is a little vauge and light on details, but here are a list of assumptions. The string is massless, the plane is frictionless, and the pully has no torque. If all of these are true then you should be able to draw a force diagram for each block

$\displaystyle F_{\text{plane}}=-mg\sin(\theta)+T$

$\displaystyle F_{\text{hang}}=mg-T$

So the net force is given by

$\displaystyle F_{net}=-mg\sin(\theta)+T+mg-T=(m+m)a_{\text{net}}$

Solving for the net acceleration gives (steps not shown)

$\displaystyle a_{net}=\frac{13}{28}g$

Now with the acceleration above and the initial velocity $\displaystyle v_0=0$ and the initial positiion $\displaystyle y_0=2$

Use the kinematic equation

$\displaystyle y-y_0=v_0t+\frac{1}{2}at^2$

to solve for the time

Re: Slope and pulley problem ? Please guide me. Thank you in advance

Thank you very much. The questions are extracted from "Understanding Mechanics". Thank you for your time and applying kinematic equation I got t= 2.82 seconds. Thank you Thank you Thank you so very much

Re: Slope and pulley problem ? Please guide me. Thank you in advance

may I know what is the value of mass?