Question

Physics EASY question

Answer 1

`m= 0.0102 \ kg\\\\\vec a = 0 \ m/s^2\\\\\sum \vec F = 0 \ N`

Step-by-step explanation:

We are given a free-body diagram of some object with two forces acting upon it.

`\vec F_(air)=0.10 \ N \ at \ 90\textdegree\\\\\vec F_(grav)=0.10 \ N \ at \ 270\textdegree`

We are asked to determine the following:

`m= \ ?? \ kg\\\vec a = \ ?? \ m/s^2\\\sum \vec F = \ ?? \ N`

`\hrulefill`

The forces are acting strictly in the y or vertical direction so we can say this:

`\sum \vec F= \vec F_(air)\sin(\theta) + \vec F_(grav)\sin(\theta)\\\\\\\Longrightarrow (0.10)\sin(90\textdegree) + (0.10)\sin(270 \textdegree)\\\\\\\Longrightarrow (0.10)(1)+ (0.10)\sin(-1)\\\\\\\Longrightarrow \sum \vec F= 0.10-0.10\\\\\\\therefore \boxed{\sum \vec F=0 \ N}`

Since the sum of these forces add to zero we can conclude that the object in question is either stationary (not moving) or moving with constant velocity (this is Newton's Second Law). Thus,

`\boxed{\vec a = 0 \ m/s^2}`

Now finding the mass of the object. We can use the following formula:

`\vec F_(grav)=mg`

Substitute what we know into the formula.

`\Longrightarrow 0.10=m(9.8)\\\\\\\Longrightarrow m=(0.10)/(9.8) \\\\\\\therefore \boxed{m\approx 0.0102 \ kg}`

Thus, all parts have been answered.