Sand is deposited at a uniform rate of 20g/s and with negligeable kinetic energy unto an empty convergor belt moving horizontally at a constant speed of 10m/s. Calculate the force required to maintain the constant velocity?

Answer 1

This is a beautiful example where I can show you,how actually Newton's 2nd Law of motion acts.

So,from Newton's 2nd Law of motion,

Force is defined as rate of change in momentum,

i,e #F=(dP)/(dt) = (d(mv))/(dt) = m (dv)/(dt) + v (dm)/(dt)# (as momentum #P=mv#)
In most of the cases,what happens mass of the object under consideration is fixed,so #(dm)/(dt) =0#,so we write, #F= m(dv)/(dt) = ma#
But,see here, #(dm)/(dt)# is not equals zero,rather #(dv)/(dt)=0# as the belt is moving with constant velocity.
so,here,required amount of force to maintain the constant velocity is #v (dm)/(dt) = 10 *(20/1000) = 0.2 N#
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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