Answer:
Torque, 
Explanation:
It is given that,
Force acting on the particle, 
Position of the particle, 
We need to find the torque on the particle about the origin. It is equal to the cross product of position and the force. Its formula is given by :
The cross product of vectors is given by :
or
So, the torque on the particle about the origin 
. Hence, this is the required solution.
<h2>
Answer: (a)t=0.553s, (b)x=110.656m</h2>
Explanation:
This situation is a good example of the projectile motion or parabolic motion, in which the travel of the bullet has two components: x-component and y-component. Being their main equations as follows:
x-component:
(1)
Where:
is the bullet's initial speed
because we are told the bullet is shot horizontally
is the time since the bullet is shot until it hits the ground
y-component:
(2)
Where:
is the initial height of the bullet
is the final height of the bullet (when it finally hits the ground)
is the acceleration due gravity
<h2>Part (a):</h2>
Now, for the first part of this problem, the time the bullet elapsed traveling, we will use equation (2) with the conditions given above:
(3)
(4)
Finding :
(5)
Then we have the time elapsed before the bullet hits the ground:
(6)
<h2>Part (b):</h2>
For the second part of this problem, we are asked to find how far does the bullet traveled horizontally. This means we have to use the equation (1) related to the x-component:
(1)
Substituting the knonw values and the value of found in (6):
(7)
(8)
Finally:
Answer:
d = 1.24 kg/m³
v = 0.81 m³/kg
Explanation:
To do this, we need to analyze the given data and know the expressions we need to use here to do calculations.
We have a pressure of 1.05 atm and 300 K of temperature. To determine the density, we need to use a similar expression of an ideal gas. In this case, instead of using moles, we will use density:
P = dRT
d = P/RT (1)
Where:
R: universal constant of gases
d: density.
From here we can determine the specific volume by using the following expression:
v = 1/d (2)
Now, as we are looking for density, we need to convert the units of pressure in atm to Pascal (or N/m) and the conversion is the following:
P = 1.05 atm * 1.013x10⁵ N/m atm = 106,365 N/m
Now, using R as 287 the density would be:
d = 106,365 / (287 * 300)
<h2>
d = 1.24 kg/m³</h2>
Finally the specific volume:
v = 1 / 1.41
<h2>
v = 0.81 m³/kg</h2>
Hope this helps
If it isn't enough energy to make the jump from 1 energy level to the next energy level, then it will go no where
" An object<span> at rest stays at rest and </span>an object <span>in motion stays in motion with the same speed and in the same direction </span>unless acted upon<span> by an </span>unbalanced force<span>."- Newtons first Law of Motion
Also, velocity is the speed of something in a given direction (So, 50mph North is an example of velocity)</span>
