 #1
 82
 0
Homework Statement
A wedge of mass 4kg and angle 30 degrees is at rest on a smooth horizontal table. a mass of 1kg is placed on the smooth inclined face of the wedge and a horizontal force of 10N is applied to towards the vertical face of the wedge. Show that the acceleration of the wedge is
(40  root(3g) ) / 17 ~= 1.35m/s.
Also find the reaction force between the wedge and the mass
Homework Equations
The Attempt at a Solution
(from diagrams)
Equation of wedge horizontally
4A = 10  Rsin30 (1)
Equation of mass horizontally
A + acos30 = Rsin30
A = Rsin30  acos30 (2)
Equation of mass vertically
asin30 = g  Rcos30 (3)
Substitute (2) into (1)
4(Rsin30  acos30) = 10  Rsin30
5Rsin30  4acos30 = 10
5Rsin30 = 10 + 4acos30
5R* 1/2 = 4a * root(3)/2 + 10
5R/2 = 2 root(3)a + 10
5R = 4root(3)a + 20
R = ((4root(3)a) / 5) + 4
Now I have 'R' in terms of 'a', but I'm not sure where to go. My notes on this trail off...I seem to substitute R back into equation (1), along with equation (2) but that will just give me R in terms of a again.
Attachments

6 KB Views: 264