Acceleration of two masses on a pulley

In summary, the correct equation for finding the acceleration of the block on the left in terms of M, m, and g is a = m*g/(m+2M) due to the tension in the string.
  • #1
wwshr87
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Homework Statement


Find the acceleration of the block on the left in terms of M, m and g.
See attachment

Homework Equations


F=ma


The Attempt at a Solution


From the free body diagram,
-Mg+Mg+mg=(m+M)*a
a=m*g/(m+M)

I think this is correct, however the solution states the correct answer as
a=m*g/(m+2M), indicating a problem with the signs.
 

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  • #2
While finding the acceleration of the masses, you have to take into account the tension in the string.

(M +m)g - T = (M+m)a...(1)

T - mg = ma. ...(2)

Now solve for a.
 

FAQ: Acceleration of two masses on a pulley

What is the definition of acceleration in the context of two masses on a pulley?

The acceleration of two masses on a pulley is the rate at which their velocity changes over time. It is a measure of how quickly the masses are speeding up or slowing down as they move along the pulley.

How is the acceleration of two masses on a pulley calculated?

The acceleration of two masses on a pulley can be calculated using the formula a = (m1-m2)g/(m1+m2), where m1 and m2 are the masses of the two objects and g is the acceleration due to gravity.

What factors affect the acceleration of two masses on a pulley?

The acceleration of two masses on a pulley is affected by the masses of the objects, the force of gravity, and the tension in the rope or string connecting the masses. Friction and air resistance may also affect the acceleration.

How does the direction of acceleration change in a system of two masses on a pulley?

The direction of acceleration in a system of two masses on a pulley can change depending on the relative masses of the objects. If the mass on one side is greater, the acceleration will be in the direction of that mass. If the masses are equal, the acceleration will be zero.

What are some real-world applications of studying the acceleration of two masses on a pulley?

Studying the acceleration of two masses on a pulley can help in understanding the principles of mechanical systems, such as pulleys and gears. It also has practical applications in industries such as manufacturing, transportation, and construction, where pulley systems are commonly used to lift and move heavy objects.

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