Quick question on Pulley Force Problems

[frownifdown]

Alright, so I'm doing this homework problem: "A 32·kg block is connected to an empty 1·kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.41 and the coefficient of kinetic friction between the table and the block is 0.34." And I need to find out the acceleration if 6.1kg of sand is put in the bucket, which I figured out is 0. Now I'm trying to find the acceleration if 7.3kg MORE is put in the bucket.

I have my Fnet as +24.696. When I put it in the equation Fnet=ma, to solve for the a, what masses do I use. Do I have it set up as 24.696=(32+13.4+1)a? Because I have that right now and it's giving me .53 which isn't the right answer. Where did I go wrong in that calculation?

 

[PhanthomJay]

Looks like your net force calculation is wrong, maybe you have made a math error. Please show how you arrived at it.
It is often not wise to look at the combined system of masses in one fell swoop . You instead should look at FBDs of each part of the system separately, getting 2 equations with 2 unknowns you can solve.

 

[johntcmb]

Once the additional 7.3 kg are added and you find that the gravitational force is enough to overcome the static frictional force, you have to use the coefficient of kinetic friction to calculate that force. That should correct the problem.

 

[frownifdown]

I actually just figured out what I did wrong. I forgot to incorporate the 1kg of the empty bucket into it. Thank you!

 

[Nickie]

Hello,

In this problem, you have correctly identified the forces acting on the system: the weight of the block, the weight of the sand, and the tension in the cord. However, the masses you are using in your calculation are incorrect. The mass of the sand should be 6.1kg, not 13.4kg, since you are only adding 6.1kg more to the existing 1kg bucket.

The correct equation to use would be: 24.696 = (32+6.1+1)a. Solving for a, we get a = 0.623 m/s^2. This means that the acceleration of the system is 0.623 m/s^2 when 7.3kg of sand is added to the bucket.

I recommend checking your calculations and making sure you are using the correct values for the masses. Double check your units as well to make sure they are consistent throughout the equation. I hope this helps!