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4 years ago

12

A railroad car moves under a grain elevator at a constant speed of 3.20 m/s. Grain drops into the car at the rate of 240 kg/min.

What is the magnitude of the force needed to keep the car moving constant speed if friction is negligible?

1 answer:

dedylja [7]4 years ago

5 0

Answer:

F = 768 N

Explanation:

It is given that,

Speed of the elevator, v = 3.2 m/s

Grain drops into the car at the rate of 240 kg/min, $\dfrac{dm}{dt}=240\ kg/min = 4\ kg/s$

We need to find the magnitude of force needed to keep the car moving constant speed. The relation between the momentum and the force is given by :

$F=\dfrac{dp}{dt}$

$F=m\dfrac{dv}{dt}+v\dfrac{dm}{dt}$

Since, the speed is constant,

$F=m\dfrac{dv}{dt}$

$F=v\dfrac{dm}{dt}$

$F=3.2\times 240$

F = 768 N

So, the magnitude of force need to keep the car is 768 N. Hence, this is the required solution.

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Read 2 more answers

The temperature of a smelting furnace is found to be 2000 ℃. Find the

IRISSAK [1]

Answer:

a) The equivalent temperature of 2000 ºC is 3632 ºF.

b) The equivalent temperature of 2000 ºC is 4091.67 R.

c) The equivalent temperature of 2000 ºC is 2273.15 K.

d) The equivalent temperature of 2000 ºC is 1600 ºRe.

Explanation:

a) The equivalent temperature on the Fahrenheit scale is defined by the following formula:

$T_{F} = \frac{9}{5}\cdot T_{C}+32$ (Eq. 1)

Where:

$T_{C}$ - Temperature, measured in degrees Celsius.

$T_{F}$ - Temperature, measured in degrees Fahrenheit.

If we know that $T_{C} = 2000\,^{\circ}C$ , then the temperature is:

$T_{F} = \frac{9}{5}\cdot (2000\,^{\circ}C)+32\,^{\circ}F$

$T_{F} = 3632\,^{\circ}F$

The equivalent temperature of 2000 ºC is 3632 ºF.

b) From result in a) we determine the equivalent temperature on the Rankine scale by using the following formula:

$T_{R} = T_{F}+459.67$ (Eq. 2)

Where:

$T_{F}$ - Temperature, measured in degrees Fahrenheit.

$T_{R}$ - Temperature, measured in Rankine.

If we know that $T_{F} = 3632\,^{\circ}F$ , then the temperature is:

$T_{R} = 3632\,^{\circ}F+459.67\,R$

$T_{R} = 4091.67\,R$

The equivalent temperature of 2000 ºC is 4091.67 R.

c) The equivalent temperature on the absolute scale is calculated by using this expression:

$T_{K} = T_{C}+273.15$ (Eq. 3)

Where:

$T_{C}$ - Temperature, measured in degrees Celsius.

$T_{K}$ - Temperature, measured in Kelvin.

If we know that $T_{C} = 2000\,^{\circ}C$ , then the temperature is:

$T_{K} = 2000\,^{\circ}C+273.15\,K$

$T_{K} = 2273.15\,K$

The equivalent temperature of 2000 ºC is 2273.15 K.

d) The equivalent temperature on the Réaumur scale is calculated by applying this expression:

$T_{Re} = \frac{4}{5}\cdot T_{C}$ (Eq. 4)

Where:

$T_{C}$ - Temperature, measured in degrees Celsius.

$T_{Re}$ - Temperature, measured in degrees Réaumur.

If we know that $T_{C} = 2000\,^{\circ}C$ , then the temperature is:

$T_{Re} = \frac{4}{5}\cdot (2000\,^{\circ}C)$

$T_{Re} = 1600\,^{\circ}Re$

The equivalent temperature of 2000 ºC is 1600 ºRe.

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