How to find the the acceleration of the block M?

In summary, the conversation discusses finding the acceleration of a block of mass M in a situation with frictionless surfaces. After some attempts at solving the problem, it is determined that the acceleration of block M is a, while the acceleration of the other block is a/2. This leads to the correct solution of a = g/3.
  • #1
avistein
48
1
1.Homework Statement
Find the acceleration of the block of mass M in the situation shown.All surfaces are frictionless

2.The attempt at a solution
2Mg-2T=2Ma
T=Mg-Ma
and T-mgsin30=ma

But a is canceled .what to do?
 

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  • #2
T=Mg-Ma

Mg-Ma-Mgsin30=Ma

2Ma = 1/2 Mg
a= 1/4 g

Not cancelled?
 
  • #3
Sorry, but answer given is g/3.
 
  • #4
Acceleration of which block is denoted by ##a##? Are the accelerations the same for both blocks?
 
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  • #5
voko said:
Acceleration of which block is denoted by ##a##? Are the accelerations the same for both blocks?

Oh,sorry.the acceleration of block 2M is a ,so acceleration of M is 2a.
 
  • #6
Do you get the answer with that correction?
 
  • #7
voko said:
Do you get the answer with that correction?

Yes sir,after Bvu's help,it is solved.
 
Last edited:
  • #8
Don't understand. In the expression T-Mgsin30=Ma a is clearly the acceleration of block M, which is what is asked for. So keep it and change the acceleration of the other block to a/2, like:

(2M)g - 2T= (2M) (a/2). Bingo!
 
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FAQ: How to find the the acceleration of the block M?

1. What is acceleration?

Acceleration is the rate of change of an object's velocity over time. It is a vector quantity, meaning it has both magnitude and direction.

2. How do you calculate acceleration?

To calculate acceleration, you divide the change in velocity by the change in time. This can be represented by the equation a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. How do you find the acceleration of a block on a horizontal surface?

To find the acceleration of a block on a horizontal surface, you need to know the net force acting on the block and its mass. Using Newton's second law, a = F/m, you can calculate the acceleration of the block.

4. How do you find the acceleration of a block on an inclined plane?

To find the acceleration of a block on an inclined plane, you need to consider the force of gravity acting on the block and its mass, as well as the angle of the incline. You can then use trigonometry to determine the component of the force of gravity acting along the incline, which can be used to calculate the acceleration.

5. How does the mass of the block affect its acceleration?

The mass of the block affects its acceleration by influencing the amount of force needed to accelerate it. The greater the mass, the more force is required to produce the same acceleration. This is represented in the equation a = F/m, where a is acceleration, F is force, and m is mass.

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