Question

Gravel is dropped on a conveyor belt at the rate of 0.5kg/s. The extra force in Newton required to keep the belt moving at 2m/s, is

Answer 1

Is it 2/0.5?

Answer 2

I am not sure.

Answer 3

are you asking 2 or 0.5?

Answer 4

Is it 2 metre/second na?

Answer 5

It's one of the option

Answer 6

which one? please do say the options.

Answer 7

(a) 1N
(b) 2N
(c) 4N
(d) 0.5 N

Answer 8

I think 2 * 0.5 = 1.

Answer 9

Can you explain it?

Answer 10

What I think is the conveyor belt is initially at rest. Gravel mass is 0.5 kg. Now given velocity is 2 m / s. So just multiplied using the force formula.

Answer 11

It is, but you need a reason behind it :D

Answer 12

I request others to check and criticize me if I am wrong.

Answer 13

force=momentum*time
so momentum is given for unit time (1 second) determine it

Answer 14

So even my answer is correct I believe.

Answer 15

the force is nevertheless 0.5N no matter how u speed up

Answer 16

Momentum is mass*velocity

Answer 17

But How?

Answer 18

Abdul, What is the correct option given in the key?

Answer 19

Key was not given

Answer 20

Oooooooooooooooo

Answer 21

sry i dint read the question properly so yes
first find momentum and then force

Answer 22

This was given in FIITJEE

Answer 23

I could know that. U can even find such questions in BMA workbook.

Answer 24

In 8th?

Answer 25

Yeah. Its actually 9th portion. Still u can try.

Answer 26

Write the net force as:
\[\ F_{net}= F - F_{thrust} \]
it is -F_thurst because the mass in increasing

The net force is zero because the system is not increasing or decreasing its velocity, that is the velocity is constant.
Now, \[\ F_{thrust}=v\frac{dm}{dt}\]

I think it is fairly easy to solve it now :D.

Answer 27

Yeah. so my answer is correct.

Answer 28

What is dm/dt?

Answer 29

change in mass per unit time or how much mass is added per second.

Answer 30

Even I will know the use of "d" in formulae in 11th grade. Can anyone explain it in detail?

Answer 31

d is a symbol for a differential. It represents an infitesimal change of some quantity (you will get to that in calculus).
It's like \[\ \Delta \] but infinitely small.

Answer 32

So, its a very tough concept. What about Calculus? I just know 2 words - Integration and Differentiation.

Answer 33

Yes that's what you do in Calculus :D. If you are impatient to learn about it I would recommend "Calculus" by Gilbert Strang

Link: http://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf