Physics, 06.07.2019 05:00 dolphin146

What is the mass of the other block?

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Answer from: kibyrd14

Let us consider the tension produced on both the sides of the rope is T.

We have been given that the rope is mass less and the rope is passing through a pulley which is stationary.

$Let\ m_{1} and\ m_{2}\ are\ the\ masses\ of\ two\ blocks$

$Let\ m_{1}\ is\ moving\ in\ vertical\ upward\ direction\ while\ m_{2}\ is\ in\ downward\ \ direction$

$Hence\ m_{2} =4.5\ kg$

The body is moving downward with an acceleration of $\frac{3}{4} g$

As the rope is the same one which is passing over a mass less pulley and connected by two masses,hence, acceleration of each block will be the same in magnitude.

$For\ body\ m_{1}$

Here the tension is acting in vertical upward direction and the weight is acting in vertical downward direction. Here,the body is moving in vertical upward direction. Hence, the net force acting on it is-

$T-m_{1} g=m_{1}a$ [1]

$For\ body\ m_{2}$

Here the tension is acting in vertical upward direction while weight is in vertical downward direction. The body is moving in downward direction. Hence the net force acting on it will be-

$m_{2} g-T=m_{2} a$ [2]

Combing 1 and 2 we get-

$T-m_{1}g=m_{1}a$

$m_{2} g-T=m_{2} a$

-------------------------------------------------

$[m_{2} -m_{1} ]g=a[m_{1}+ m_{2}]$

$[4.5-m_{1}]g =\frac{3}{4}g[4.5+ m_{1}]$

$4[4.5-m_{1}] =3[4.5+m_{1} ]$

$7m_{1} =4.5 kg$

$m_{1} = 0.64286 kg$ [ans]

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

Answer from: Quest

total distance/total time

(85 + 82)/(5+3)

167/8

20 just over

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