Solving for acceleration of two blocks with two pulleys

Thread starter Che8833
Start date Apr 1, 2019
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Acceleration Blocks Pulleys Two blocks

In summary, the formula for solving for acceleration in a system of two blocks and two pulleys is a = (m1-m2)/(m1+m2). The direction of acceleration in this type of system can be determined by analyzing the tension forces on each block, with the block experiencing the greater tension force accelerating in that direction. The acceleration of the two blocks can be different if the masses or tension forces are not equal. To calculate the tension forces, the formula T = ma can be used, with the acceleration found using the first question's formula. Factors such as block masses, coefficients of friction, pulley angle, and external forces can affect the acceleration in this type of system.

Apr 1, 2019

Che8833

Homework Statement: If block A has mass M and block b has mass m, find the acceleration of block B assuming that the acceleration of block A equals two times the acceleration of block B.

Relevant Equations: Equation 1: T = Ma1

Equation 2: mg - 2T = ma2

Equation 3: a1 = 2a2

Equation 1: T = Ma1

Equation 2: mg - 2T = ma2

Equation 3: a1 = 2a2

Since a1 = 2a for equation one I get T = 2Ma1

mg - 4Ma1 = ma1

mg = 4Ma1 + ma1

mg = 4a1(M+m)

a1= mg / 4M+m

Not sure if this is correct. Can someone please help to make sure I'm doing this right?
Thanx

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Apr 1, 2019

quinoa19

Looks correct, I got same answer,
##a_{\rm B}=\frac{mg}{m+4M} ##

What is the concept of acceleration in relation to two blocks with two pulleys?

The concept of acceleration in this scenario refers to the rate of change of velocity of the two blocks as they move due to the forces exerted by the two pulleys.

How do you calculate the acceleration of the two blocks?

To calculate the acceleration, you would need to know the mass and net force acting on each block. Using Newton's second law of motion (F=ma), you can calculate the acceleration of each block individually and then compare them to find the overall acceleration of the system.

What factors can affect the acceleration of the two blocks?

The acceleration of the two blocks can be affected by various factors such as the mass of the blocks, the angle of the pulleys, the coefficient of friction between the blocks and the surface they are on, and any external forces acting on the system.

How does the use of pulleys affect the acceleration of the two blocks?

The use of pulleys can change the direction and magnitude of the forces acting on the blocks, which in turn can affect the acceleration. By using multiple pulleys, the force can be distributed evenly between the two blocks, resulting in a more efficient system with a lower overall acceleration.

What are the applications of solving for the acceleration of two blocks with two pulleys in real-world scenarios?

This concept has various applications in real-world scenarios such as in elevators, cranes, and construction equipment. It also plays a crucial role in understanding the mechanics of machines and in designing pulley systems for efficient and safe operations.