Motion in A Plane

Physics Part I

Physics

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A balloon with mass m is descending down with an acceleration a (where a <g). How much mass should be removed from it so that it starts moving up with an acceleration a?

A.

When the balloon is descending down with acceleration a,

So, mg - B = mx A Â Â Â Â Â Â ... (i)

where B is the buoyant force.

We assume here that while removing same mass, the volume of balloon and hence buoyant force will not change.

Let, us assume the new mass of the balloon is m'.

So, mass removed is (m-m')

Therefore,

B-m'g = m'x a Â Â Â Â ... (ii)

On solving equations (i) and (ii), we have

mg - B = m x a

B - m'g = m' x a

mg - m'g = ma + Â m'a

(mg - ma) = m' (g+a) = m (g-a) = m' (g+a)

That is,

That is, mass removed is m-m'

When the balloon is descending down with acceleration a,

So, mg - B = mx A Â Â Â Â Â Â ... (i)

where B is the buoyant force.

We assume here that while removing same mass, the volume of balloon and hence buoyant force will not change.

Let, us assume the new mass of the balloon is m'.

So, mass removed is (m-m')

Therefore,

B-m'g = m'x a Â Â Â Â ... (ii)

On solving equations (i) and (ii), we have

mg - B = m x a

B - m'g = m' x a

mg - m'g = ma + Â m'a

(mg - ma) = m' (g+a) = m (g-a) = m' (g+a)

That is,

That is, mass removed is m-m'

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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.

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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors.Â

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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.

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