Three masses suspended on pulley

  • Thread starter gap0063
  • Start date
  • Tags
    Pulley
In summary, The pulley is massless and frictionless, with 3 kg, 2 kg, and 6 kg masses suspended. Using the equations T2-m1g=m1a, m2g+T1-T2=m2a, and m3g-T1=m3a, we can combine them to solve for the acceleration as a=4.45455 m/s^2. This value is then plugged into T1=m3g-m3a to get T1=32.0727N (right). However, there is a signage error in the 2nd relevant equation where the weight acts down, so it should have a minus sign in front of it. After correcting this, the acceleration is
  • #1
gap0063
65
0

Homework Statement


A pulley is massless and frictionless. 3 kg, 2 kg, and 6 kg masses are suspended on a pulley.

(a)What is the tension T1 in the string between the two blocks on the left-hand side of the pulley?

(b)What is the magnitude of the acceleration of the lower left-hand block?



Homework Equations


I solved for (a) using the equations:
T2-m1g=m1a
m2g+T1-T2=m2a
m3g-T1=m3a


The Attempt at a Solution



the combining those equations:
-m1g+m2g+m3g=m1a+m2a+m3a

then I solved for a
-29.4+19.6+58.8=11a
a=4.45455 m/s^2

then plugged into T1=m3g-m3a and got T1=32.0727N (right

for part (b) I thought that I already had a since I needed it to slove for T1, but it is wrong...

So does the lower left-hand block have a different acceleration?


Also, I tried putting in -4.45455 m/s^2 since m3 is 6kg and ways more than m1 and m2 combined... also didn't work
 
Physics news on Phys.org
  • #2
You have a signage error in your 2nd relevant equation...the weight acts down, so it should have a minus sign in front of it. Redo your calc for the acceleration and value of T1.
 
  • #3
PhanthomJay said:
You have a signage error in your 2nd relevant equation...the weight acts down, so it should have a minus sign in front of it. Redo your calc for the acceleration and value of T1.

In front of the whole equation or just infront of all m2?
 
  • #4
gap0063 said:
In front of the whole equation or just infront of all m2?

Well, just in front of m2...on the left side of the equation, the weight acts down, and T2 acts down , so both those terms are minus; T1 acts up, so that's plus; on the right side of the equation, the acceleration is up, so that's a plus sign.
 
  • #5
PhanthomJay said:
Well, just in front of m2...on the left side of the equation, the weight acts down, and T2 acts down , so both those terms are minus; T1 acts up, so that's plus; on the right side of the equation, the acceleration is up, so that's a plus sign.

What about m2 in front of acceleration?
 
  • #6
gap0063 said:
What about m2 in front of acceleration?

Repeat...positive.
 

Related to Three masses suspended on pulley

1. How does the pulley system work?

The pulley system works by using a combination of ropes, wheels, and other mechanisms to redirect and distribute the force of gravity. In the case of three masses suspended on a pulley, the system is designed to evenly distribute the weight and tension between the three masses, allowing them to move in a coordinated manner.

2. What are the equations used to calculate the forces in a three masses suspended on pulley system?

The equations used to calculate the forces in a three masses suspended on pulley system are derived from Newton's laws of motion and include the equations for static equilibrium and the equations for the tension in the ropes or strings attached to the masses.

3. How does the mass of the pulley affect the system?

The mass of the pulley can affect the system in several ways. A heavier pulley may require more force to move the masses, and may also increase the tension in the ropes or strings. Additionally, the mass of the pulley can affect the overall stability and balance of the system.

4. What is the role of friction in a three masses suspended on pulley system?

Friction plays a crucial role in a three masses suspended on pulley system. The friction between the ropes or strings and the pulley, as well as between the ropes themselves, helps to keep the system in equilibrium and prevents the masses from moving too quickly or uncontrollably.

5. How does the angle of the ropes or strings affect the forces in a three masses suspended on pulley system?

The angle of the ropes or strings can have a significant impact on the forces in a three masses suspended on pulley system. As the angle increases, the tension in the ropes or strings also increases, which can affect the overall stability and balance of the system. Additionally, different angles can result in different equations and calculations for the forces in the system.

Similar threads

Accelerating pulleys (3 pulleys and 3 masses)
Replies
5
Views
1K
Block-pulley system and rotational dynamics
Replies
5
Views
5K
Angular Acceleration and Linear Acceleration of a Pulley
Replies
4
Views
1K
Pulleys with Torque: Free Body Diagram Analysis
Replies
34
Views
2K
I have a question about a pulley and tension-related problem
Replies
3
Views
1K
Calculating tensions and acceleration
Replies
10
Views
2K
Problem with two pulleys and three masses
3
Replies
102
Views
5K
Finding Tensions and Accelerations with Moveable Pulley
Replies
5
Views
1K
Finding tension and acceleration in a 3 weight, 3 pulley system
Replies
4
Views
7K
Halliday, Resnick & Krane Chapter 5: Force on Pulley
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top