# Momentum

#### werehk

PHF Hall of Fame
A block of mass $$\displaystyle m$$ is connected to a motor by a string. The string is connected to the pulley inside the motor. The block is accelerating towards the motor on a smooth level surface.

Accounting for the increase in momentum of block,

why is it transferred from the momentum of the Earth to the block?

Why it is not due to kinetic energy transfer from the motor?

#### topsquark

Forum Staff
A block of mass $$\displaystyle m$$ is connected to a motor by a string. The string is connected to the pulley inside the motor. The block is accelerating towards the motor on a smooth level surface.

Accounting for the increase in momentum of block,

why is it transferred from the momentum of the Earth to the block?

Why it is not due to kinetic energy transfer from the motor?
Both of these answers essentially boil down to the same principle: Newton's 3rd Law. The motor is exerting a force F on the block, so the block exerts a force F on the motor. So for the motor to be stationary, we need a counterforce F acting on it from the ground. Thus the action of the motor essentially transfers the force F on the block to the ground. Since the ground now has a force on it, there is a torque on the Earth, and thus the Earth's momentum is changing.

-Dan

werehk

#### werehk

PHF Hall of Fame
I'm quite confused. Could you draw a diagram for me indicating forces on block , motor and the ground?(Sweating)

#### topsquark

Forum Staff
In all it's glory then.

There is a tension force on the block due to the motor. ($$\displaystyle T_{bm}$$) Newton's 3rd says there must be a force acting in the opposite direction acting on the motor. ($$\displaystyle T_{mb}$$)

For the motor not to move it must be connected to the ground (table, whatever). Because the motor is not accelerating we can say, from Newton's 2nd that there exists a force equal and opposite to $$\displaystyle T_{mb}$$ acting on the motor due to the Earth: $$\displaystyle F_{mE}$$. (This is NOT a third law pair to $$\displaystyle T_{mb}$$ even though it is equal and opposite to it.) Since there is a force on the motor by the Earth, the Earth must have a force on it by the motor $$\displaystyle F_{Em}$$ (not shown in diagram.) Since there is a force on the Earth the Earth's momentum is changing, etc.

-Dan

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