Two masses connected by string on 40° incline with friction

[jwxie]

Homework Statement

Masses m1 = 4.0kg and m2 = 9.0kg are connected by a light string that passes over a frictionless pulley. As shown in Figure, m1 is held at rest on the floor and m2 rests on a fixed incline of 40 degree. The masses are released from rest, and m2 slides 1.00m down the incline in 4.00s.

Determine a) the acceleration of each mass b) the tension in the string and c) the coefficient of kinetic friction between m2 and the incline.

Homework Equations

Fnet = ma
distance formula
d = 1/2at^2 when vi = 0

The Attempt at a Solution

Well, I know the acceleration for m2 is 0.125m/s^2 using the distance formula when vi=0.
but then i got stuck at the rest, i tried to find acceleration of m1 but didn't work out at all.

well if i tried
m2gcos - m1g = m2a1+m1a2
(since incline plane i can find fg by m2gCos)
but the problem is, i totally ignore the friction Ff i think...
this is why i come up with answer like 6.8m/s^2 for mass1.

the rest will be wrong if i can't set up a system of equation for #1
i tried, like

m2gCos + Ft = m2a
m1g + (-Ft) = m1a

Ft means force of tension

 

[hage567]

You need to consider the forces on each mass separately. Remember, force is a vector.

Start by considering just the mass on the incline. Draw a free body diagram. What forces are present? Write out an equation for each direction (take the x direction to be along the incline and the y direction to be perpendicular to the incline).

Now do the same for the other mass. This one is much easier, since there are only forces in one direction.

From this you will get a set of equations that you can use to solve for what you need to find.