Atwood's Machine: Finding Acceleration & Tension Magnitudes

In summary, an Atwood's machine consists of two blocks, A and B, connected by a string that moves over a wheel with a radius R. The masses of the blocks are m_A and m_B respectively, and the moment of inertia of the wheel is I. The linear acceleration of block A is found by the equation m_A*a = m_A*g - T_A, while the linear acceleration of block B is found by m_B*a = T_B - m_B*g. The angular acceleration of the wheel is calculated using the equation I(alpha) = T_A*R - T_B*R. The tension in the left and right sides of the cord can be found by considering the no slipping condition between the cord and the wheel's surface
  • #1
Tonyt88
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There is an Atwood's machine. The masses of blocks A and B are m_A and m_B, respectively, the moment of inertia of the wheel about its axis is I, and the radius of the semicircle in which the string moves is R.

Known: m_A > m_B

a)Find the magnitude of the linear acceleration of the block A.
b)Find the magnitude of the linear acceleration of the block B.
c)What is the magnitude of the angular acceleration of the wheel C?
d)Find the magnitude of the tension in the left side of the cord if there is no slipping between the cord and the surface of the wheel.
e)Find the magnitude of the tension in the right side of the cord if there is no slipping between the cord and the surface of the wheel.

Okay, so I have:

m_A*a = m_A*g - T_A

m_B*a = T_B -m_B*g

I(alpha) = T_A*R - T_B*R

a = R(alpha)

Am I missing something, or...
 
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  • #2

FAQ: Atwood's Machine: Finding Acceleration & Tension Magnitudes

What is an Atwood's Machine?

An Atwood's Machine is a simple mechanical device used to study the principles of motion and forces in physics. It consists of two masses connected by a string or rope over a pulley, with one mass hanging on each side of the pulley.

How do you find the acceleration and tension magnitudes in an Atwood's Machine?

The acceleration can be found by using the equation a = (m1 - m2)g / (m1 + m2), where m1 and m2 are the masses on either side of the pulley and g is the acceleration due to gravity. The tension magnitude can be calculated using the equation T = m1a + m1g, where T is the tension in the string and m1 is the mass on one side of the pulley.

What factors affect the acceleration and tension magnitudes in an Atwood's Machine?

The acceleration and tension magnitudes in an Atwood's Machine are affected by the masses of the objects, the gravitational acceleration, and the friction in the pulley. They can also be affected by external forces such as air resistance or the angle of the string over the pulley.

How does an Atwood's Machine demonstrate Newton's Second Law of Motion?

An Atwood's Machine demonstrates Newton's Second Law of Motion, also known as the law of acceleration, by showing that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this case, the net force is the difference in weight between the two masses and the acceleration is determined by the masses and the gravitational acceleration.

What are some real-world applications of Atwood's Machine?

Atwood's Machine has various real-world applications, such as elevators and cranes that use pulley systems to lift heavy objects. It is also used in physics classrooms as a teaching tool to demonstrate concepts like motion, forces, and Newton's Laws. Additionally, Atwood's Machine can be used to measure the value of gravitational acceleration in a specific location.

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