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

• Oct 15th 2012, 03:01 AM
mysur
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?
• Oct 15th 2012, 04:48 AM
TheEmptySet
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

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

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

So the net force is given by

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

Solving for the net acceleration gives (steps not shown)

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

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

Use the kinematic equation

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

to solve for the time
• Oct 15th 2012, 09:44 AM
mysur
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
• Oct 15th 2012, 01:10 PM
mysur
Re: Slope and pulley problem ? Please guide me. Thank you in advance
may I know what is the value of mass?