Question

help me!
A 5.00 kg block on a 30 degree incline is connected by a light string over a frictionless pulley to an unknown mass, m. The coefficient of kinetic friction between the block and the incline is 0.100. When the system is released from rest, mass m accelerates upward at 2.0 m/s2.
determine the string tension and value of m.

Answer 1

Darw The Physical Situation First..

Answer 2

let the mass on the incline be M. and the mass hanging is m.
let the acceleration given be a.
let the tension in the string be T.
so for the mass M on the incline which is accelerating down the incline with acceleration a,
we have,

\[Mgsin30 - T - \mu*R = M*a\]

and
\[R = Mgcos30\]

hence combining we get,
\[Mgsin30 - T - \mu*mgcos30 = M*a\] --Eq.1

now lets look at the mass m, which is hanging and is accelerating vertically upwards with the same acceleration a.

\[T - mg = m*a\]

--Eq.2

add Eq1. and Eq2. to get m

\[Mgsin30 - \mu*mgcos30 - mg = a*(M + m)\]

\[m = M(gsin30 - a)/(g + \mu*gcos30 + a)\]

comes out to be,
m = 1.15 kg

similarly calculate Tension by substracting Eq1. from Eq2.