Answer:
Good question to ask in physics, sir maam
Answer:
a) The x coordinate of the third mass is -1.562 meters.
b) The y coordinate of the third mass is -0.944 meters.
Explanation:
The center of mass of a system of particles (
), measured in meters, is defined by this weighted average:
(1)
Where:
- Mass of the i-th particle, measured in kilograms.
- Location of the i-th particle with respect to origin, measured in meters.
If we know that
,
,
,
,
and
, then the coordinates of the third particle are:
![(-0.500\,m, -0.700\,m) = \frac{(1\,kg)\cdot (-1.20\,m,0.500\,m)+(4.50\,kg)\cdot (0.600\,m,-0.750\,m)+(4\,kg)\cdot \vec r_{3}}{1\,kg+4.50\,kg+4\,kg}](https://tex.z-dn.net/?f=%28-0.500%5C%2Cm%2C%20-0.700%5C%2Cm%29%20%3D%20%5Cfrac%7B%281%5C%2Ckg%29%5Ccdot%20%28-1.20%5C%2Cm%2C0.500%5C%2Cm%29%2B%284.50%5C%2Ckg%29%5Ccdot%20%280.600%5C%2Cm%2C-0.750%5C%2Cm%29%2B%284%5C%2Ckg%29%5Ccdot%20%5Cvec%20r_%7B3%7D%7D%7B1%5C%2Ckg%2B4.50%5C%2Ckg%2B4%5C%2Ckg%7D)
![(-4.75\,kg\cdot m, -6.65\,kg\cdot m) = (-1.20\,kg\cdot m, 0.500\,kg\cdot m) + (2.7\,kg\cdot m, -3.375\,kg\cdot m) +(4\cdot x_{3},4\cdot y_{3})](https://tex.z-dn.net/?f=%28-4.75%5C%2Ckg%5Ccdot%20m%2C%20-6.65%5C%2Ckg%5Ccdot%20m%29%20%3D%20%28-1.20%5C%2Ckg%5Ccdot%20m%2C%200.500%5C%2Ckg%5Ccdot%20m%29%20%2B%20%282.7%5C%2Ckg%5Ccdot%20m%2C%20-3.375%5C%2Ckg%5Ccdot%20m%29%20%2B%284%5Ccdot%20x_%7B3%7D%2C4%5Ccdot%20y_%7B3%7D%29)
![(4\cdot x_{3}, 4\cdot y_{3}) = (-6.25\,kg\cdot m,-3.775\,kg\cdot m)](https://tex.z-dn.net/?f=%284%5Ccdot%20x_%7B3%7D%2C%204%5Ccdot%20y_%7B3%7D%29%20%3D%20%28-6.25%5C%2Ckg%5Ccdot%20m%2C-3.775%5C%2Ckg%5Ccdot%20m%29)
![(x_{3},y_{3}) = (-1.562\,m,-0.944\,m)](https://tex.z-dn.net/?f=%28x_%7B3%7D%2Cy_%7B3%7D%29%20%3D%20%28-1.562%5C%2Cm%2C-0.944%5C%2Cm%29)
a) The x coordinate of the third mass is -1.562 meters.
b) The y coordinate of the third mass is -0.944 meters.
Answer:
109656.25 Nm
Explanation:
= Final angular velocity = 1.5 rad/s
= Initial angular velocity = 0
= Angular acceleration
t = Time taken = 6 s
m = Mass of disk = 29000 kg
r = Radius = 5.5 m
![\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\dfrac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\dfrac{1.5-0}{6}\\\Rightarrow \alpha=0.25\ rad/s^2](https://tex.z-dn.net/?f=%5Comega_f%3D%5Comega_i%2B%5Calpha%20t%5C%5C%5CRightarrow%20%5Calpha%3D%5Cdfrac%7B%5Comega_f-%5Comega_i%7D%7Bt%7D%5C%5C%5CRightarrow%20%5Calpha%3D%5Cdfrac%7B1.5-0%7D%7B6%7D%5C%5C%5CRightarrow%20%5Calpha%3D0.25%5C%20rad%2Fs%5E2)
Torque is given by
![\tau=I\alpha\\\Rightarrow \tau=\dfrac{1}{2}mr^2\alpha\\\Rightarrow \tau=\dfrac{1}{2}29000\times 5.5^2\times 0.25\\\Rightarrow \tau=109656.25\ Nm](https://tex.z-dn.net/?f=%5Ctau%3DI%5Calpha%5C%5C%5CRightarrow%20%5Ctau%3D%5Cdfrac%7B1%7D%7B2%7Dmr%5E2%5Calpha%5C%5C%5CRightarrow%20%5Ctau%3D%5Cdfrac%7B1%7D%7B2%7D29000%5Ctimes%205.5%5E2%5Ctimes%200.25%5C%5C%5CRightarrow%20%5Ctau%3D109656.25%5C%20Nm)
The torque specifications must be 109656.25 Nm
Answer:
Time, t = 0.87 seconds
Explanation:
Given that,
Initial velocity of the object, u = 4.3 m/s
The coefficient of kinetic friction between horizontal tabletop and the object is 0.5
We need to find the time taken by the object for the object to come to rest i.e. final velocity will be 0.
Using first equation of motion to find it as :
![v=u+at](https://tex.z-dn.net/?f=v%3Du%2Bat)
a is the acceleration, here, ![a=\mu g](https://tex.z-dn.net/?f=a%3D%5Cmu%20g)
![0=u+\mu gt](https://tex.z-dn.net/?f=0%3Du%2B%5Cmu%20gt)
![t=\dfrac{u}{\mu g}\\\\t=\dfrac{4.3}{0.5\times 9.8}\\\\t=0.87\ s](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7Bu%7D%7B%5Cmu%20g%7D%5C%5C%5C%5Ct%3D%5Cdfrac%7B4.3%7D%7B0.5%5Ctimes%209.8%7D%5C%5C%5C%5Ct%3D0.87%5C%20s)
So, the time taken by the object to come at rest is 0.87 seconds. Hence, this is the required solution.