# Homework Help: Find the largest mass that can sit on an incline without accelerating

1. Sep 26, 2010

### vande060

1. The problem statement, all variables and given/known data
A mass M1 = 10 kg rests on an incline of
angle θ = 60deg. Find the largest M2 such that no
accelerations occur.

a picture of the problem: http://s861.photobucket.com/albums/ab174/alkaline262/?action=view&current=prob14.jpg

2. Relevant equations

f=ma

3. The attempt at a solution

here are the forces for m1(i think)

note: N is normal force T is string tension

(-a1,0) (0,N) (-m1gsin(60), -mg1cos(60)) (T1,0)
---------------------------------------------------
equations here for m1:

-m1a1 = T1 -m1gsin(60)
0 = N- m1gcos(60)
--------------------------------------------------
here are the forces for m2(i think)

(0,-a2) (0,T2) (0,-m2g)

-------------------------------------------------
equation for m2:

-m2a = T2 -m2g
--------------------------------------------------

all right now, i feel like i should be eliminating T, because it will be equal between the two equations:

T1 = -m1a + sin(60)m1g
- T2 = -m2a + m2g
-----------------------------
0 = -m1a + m2a +sin(60)m1g - m2g

okay i dont know what to do, or if what i have done is right, but i let a = 0 and solved for m2 here anyways :/

m2 = sin(60)m1
we know m1 = 10 so,

max m2 = 8.7 kg

2. Sep 27, 2010

### The legend

an easier way would be taking the g components for m1 and since the (perpendicular-to-the-plane component) is balanced by normal reaction you can neglect it. Then the {along-the-inlinedplane(say gx) * mass1} should be equated to (mass2 * g) . and then get the answer easily...
ie
m1 * gx = m2 * g