Why does 2T-(M+m)g=(M+m)a not work here?

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The equation 2T - (M+m)g = (M+m)a is incorrect because it does not account for the equal and opposite force exerted on the platform when the man pulls on the rope. The correct force P required to achieve acceleration a is (m+M)(a+g), not (m+M)(a+g)/2. The platform exerts an equal and opposite normal force, necessitating a greater force to accelerate the combined mass of the man and platform. The tension in the rope contributes to the upward force, which is why the total force is represented as 2P. Understanding these dynamics clarifies the relationship between the forces involved in the system.
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Can someone explain why the force P with which the man must pull on the rope to achieve an acceleration a m/s2 IS NOT (m+M)(a+g)/2 and is instead (m+M)(a+g). M+m is the combined mass of man and platform.

Why does 2T-(M+m)g=(M+m)a not work here?
 

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when he pulls the rope, an equal and opposite force is exerted on the platform.
 
Thanks for the response. But doesn't the platform have an equal and opposite normal force?
 
Exactly why greater force is required to accelerate the mass of the man + platform.

2P=(m+M)(g+a)+P
 
but doesn't the tension of the rope on the other side contribute just as much as the man therefore doubling the total force upwards?
 
Yes, and that is the only reason he can lift himself. This is why the left is 2P.
 

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