Calculating Tension and Acceleration in a Two-Pulley System

In summary, the individual is seeking help in solving for T1, T2, a1, and a2 in a system involving two blocks connected to two pulleys. They share that they have tried using a derived formula and that they know certain equations, but are unsure of how to use them with Newton's 2nd law. After some guidance, they are able to set up equations for each mass and solve for the unknowns to find a correct solution.
  • #1
savelieffd
7
0
Hope someone can help me with this one. I have two blocks with m1 and m2 connected to two pulleys. I need to figure out T1, T2, a1, and a2 using only the values of g, m1, and m2. But I've been unable to come up with an equation that will work with it. I have a picture attached.

I tried using the following expression: ((m2*g)-(m1)*g)/(m1+m2) to find a1, but that didnt work and I am stumped. does anyone have any ideas? any help would be great!


http://img292.imageshack.us/img292/374/p438ym8.gif
 
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  • #2
Instead of trying to force fit some derived formula, use Newton's 2nd law. Analyze the forces acting on each mass and set up equations of motion for each. Hint: How does the acceleration of m1 compare to m2? How does the tension T1 compare to T2?
 
  • #3
well i know that a1 = 2 *a2, and i know that T2 = 2 *T1. But i don't know how i can put these together to work with Newtons 2nd law.
 
  • #4
savelieffd said:
well i know that a1 = 2 *a2, and i know that T2 = 2 *T1.
Good.
But i don't know how i can put these together to work with Newtons 2nd law.
What forces act on each mass? Set the net force equal to ma! (Careful with signs.)

You'll get a separate equation for each mass. Combine to solve for your unknowns.
 
  • #5
Would m1 accelerate at 2*g? BEcause of the pulley?
 
  • #6
Don't guess or try to do it in your head. Write the equations and then solve them.
 
  • #7
Because of the frictionless surface, would the net force be just the tension? If so, would a1 = ((m1*m2*(Sin(theta)+1)*g)/(m1+m2))/m1) and Sin(theta) equals 1 becuase theta is equal to 90?
 
  • #8
savelieffd said:
Because of the frictionless surface, would the net force be just the tension?
Net force on what? Which tension?

(Write the equations.)
 
  • #9
Aha, revelation. Looks like i figured it out!

T1 = (m1*m2)/(2m1 + .5m2)*g

then

T2 = (m1*m2)/(m1 + .25m2)*g

yes?

and using the equations of tension,

a1 = t1/m1 = (m2*g)/(2m1 +.5m2)

and so a2 = half of a1 which is = (m2*g)/(4m1+m2)

and in the end we get a correct answer for all of them! Brilliant!

Thanks so much!
 

FAQ: Calculating Tension and Acceleration in a Two-Pulley System

1. How do two pulleys and two blocks work together?

The two pulleys and two blocks system is a mechanical system that utilizes the principles of pulleys and tension to transfer force and motion between two blocks. The two pulleys serve as a means to change the direction of the force, while the blocks are connected by a rope or belt that is looped around the pulleys. As one block moves, the other block will move in the opposite direction, creating a force balance between the two blocks.

2. What is the purpose of using two pulleys in this system?

The use of two pulleys in this system allows for the force to be redirected and spread out over a longer distance. This reduces the amount of force needed to lift or move an object, making it easier for humans to perform tasks that require a lot of force. Additionally, using two pulleys also increases the mechanical advantage of the system, making it more efficient.

3. Can the position of the pulleys affect the system's performance?

Yes, the position of the pulleys can affect the system's performance. The ideal position for the pulleys is in a straight line, as this allows for the most efficient transfer of force and motion between the two blocks. If the pulleys are not in a straight line, it can create unnecessary friction and decrease the mechanical advantage of the system.

4. How do the masses of the two blocks affect the system's behavior?

The masses of the two blocks do not affect the system's behavior as long as the ratio of their masses remains the same. This is because the tension in the rope or belt connecting the blocks will adjust to accommodate the different masses, creating a force balance between the two blocks. However, if the masses of the blocks are significantly different, it can affect the tension in the rope and the overall performance of the system.

5. Are there any real-world applications of the two pulleys and two blocks system?

Yes, there are many real-world applications of the two pulleys and two blocks system. One common example is in elevators, where two pulleys and two blocks are used to lift and lower the elevator car. Another example is in exercise equipment such as weightlifting machines, where pulleys and blocks are used to create resistance and make it easier for users to lift heavy weights.

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