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

[physicstime]

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?

 

[JustinRyan]

when he pulls the rope, an equal and opposite force is exerted on the platform.

 

[physicstime]

Thanks for the response. But doesn't the platform have an equal and opposite normal force?

 

[JustinRyan]

Exactly why greater force is required to accelerate the mass of the man + platform.

2P=(m+M)(g+a)+P

 

[physicstime]

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?

 

[JustinRyan]

Yes, and that is the only reason he can lift himself. This is why the left is 2P.