Pulley problem: sand being poured into a bucket tied to a block

[N_L_]

I am having trouble setting up the following problem. I can work it out if there is no acceleration, however with acceleration it seems like there are too many variables.

http://img160.imageshack.us/img160/9126/untitled4bd.jpg

What I have so far:



mass of block = 28 kg = Mblock
mass of sand = total mass of filled bucket - 1.35 kg = Msand
acceleration = a
Force tension = Ft
Force friction = Ffr

The two objects will have the same Ft and the same acceleration.

The sum of the forces in the X direction = Ft - Ffr = Mblock * a
The sum of the forces in the Y direction = Msand*g - Ft = Msand*a

Am I correct in thinking that since just enough sand is being added to make the block move, that the friction being used is static friction...to determine the amount of sand that needs to be added?

 

[phucnv87]

Consider
$\mu=0.45$, $k=0.32$, $M=28kg$, $m_0=1.35kg$, $m=m_{Sand}$
a) $(m_0+m)g=\mu Mg$
b) $(m_0+m)g-kMg=(M+m_0+m)a$

 

[kyle8921]

Great job on identifying the variables and forces involved in this problem! You are correct in thinking that the friction being used is static friction, as the block and bucket are not moving relative to each other.

To solve this problem, you will need to use Newton's second law, which states that the sum of the forces acting on an object is equal to its mass times its acceleration (ΣF=ma). In this case, there are two objects (the block and the bucket of sand) with different masses but the same acceleration, so we will need to set up two equations and solve them simultaneously.

First, let's look at the block. The only forces acting on it are the tension force (Ft) and the friction force (Ffr). Using Newton's second law, we can set up the following equation:
Mblock * a = Ft - Ffr

Next, let's look at the bucket of sand. The forces acting on it are the weight of the sand (Msand * g), the tension force (Ft), and the normal force (Fn) from the block. Since the bucket is not moving vertically, the sum of the forces in the Y direction must equal zero. Using this information, we can set up the following equation:
0 = Msand * g - Ft - Fn

Now, we need to find the value of the normal force (Fn) in order to solve for the tension force (Ft). We can do this by using Newton's second law again on the block:
Mblock * a = Ft - Ffr
Since we know that the friction force is equal to the normal force (Ffr = Fn), we can substitute this into our equation:
Mblock * a = Ft - Fn
Rearranging this equation, we get:
Fn = Ft - Mblock * a

Now, we can substitute this value for Fn into our equation for the bucket of sand:
0 = Msand * g - Ft - (Ft - Mblock * a)
Simplifying, we get:
0 = Msand * g - 2Ft + Mblock * a

Now, we have two equations and two unknowns (Ft and a) that we can solve using algebra. Once we have solved for the tension force, we can use this value to find the amount of sand needed to make the block move.

I hope this helps and