Answer:
Consult not your fears but your hopes and your dreams. Think not about your frustrations, but about your unfulfilled potential. Concern yourself not with what you tried and failed in, but with what it is still possible for you to do.
Answer:
Explanation:
m1 = 3.77 kg (0, 0 )
m2 = 6.7106 kg ( 5.72 cm, 11.44 cm)
m3 = 2.46181 kg (16.7024 cm, 0 cm )
Let x and y be the coordinates of centre of mass.
![x = \frac{m_{1}x_{1}+ m_{2}x_{2}+m_{3}x_{3}}{m_{1}+m_{2}+m_{3}}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7Bm_%7B1%7Dx_%7B1%7D%2B%20m_%7B2%7Dx_%7B2%7D%2Bm_%7B3%7Dx_%7B3%7D%7D%7Bm_%7B1%7D%2Bm_%7B2%7D%2Bm_%7B3%7D%7D)
![x = \frac{3.77\times 0+ 6.7106\times 5.72 + 2.46181\times 16.7024}{3.77+6.7106+2.46181}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B3.77%5Ctimes%200%2B%206.7106%5Ctimes%205.72%20%2B%202.46181%5Ctimes%2016.7024%7D%7B3.77%2B6.7106%2B2.46181%7D)
x = 6.1428 cm
![y = \frac{m_{1}y_{1}+ m_{2}y_{2}+m_{3}y_{3}}{m_{1}+m_{2}+m_{3}}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7Bm_%7B1%7Dy_%7B1%7D%2B%20m_%7B2%7Dy_%7B2%7D%2Bm_%7B3%7Dy_%7B3%7D%7D%7Bm_%7B1%7D%2Bm_%7B2%7D%2Bm_%7B3%7D%7D)
![y= \frac{3.77\times 0+ 6.7106\times 11.44 + 2.46181\times 0}{3.77+6.7106+2.46181}](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B3.77%5Ctimes%200%2B%206.7106%5Ctimes%2011.44%20%2B%202.46181%5Ctimes%200%7D%7B3.77%2B6.7106%2B2.46181%7D)
y = 5.9316 cm
Answer:
![\vec{F} = -0.34\^x - 0.22\^y\\|\vec{F}| = -0.41~N](https://tex.z-dn.net/?f=%5Cvec%7BF%7D%20%3D%20-0.34%5C%5Ex%20-%200.22%5C%5Ey%5C%5C%7C%5Cvec%7BF%7D%7C%20%3D%20-0.41~N)
Explanation:
The electric force between two point charges can be calculated by Coulomb's Law:
![\vec{F} = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}\^r](https://tex.z-dn.net/?f=%5Cvec%7BF%7D%20%3D%20%5Cfrac%7B1%7D%7B4%5Cpi%5Cepsilon_0%7D%5Cfrac%7Bq_1q_2%7D%7Br%5E2%7D%5C%5Er)
We have to calculate the distance between two points; (0,0) and (0.3 m, 0.2 m).
![r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(0.3)^2 + (0.2)^2} = 0.36~m](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%20%3D%20%5Csqrt%7B%280.3%29%5E2%20%2B%20%280.2%29%5E2%7D%20%3D%200.36~m)
Now we can apply Coulomb's Law
![F = \frac{1}{4\pi\epsilon_0}\frac{(3\times 10^{-6})(-2\times 10^{-6})}{(0.36)^2} = -0.41~N](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B1%7D%7B4%5Cpi%5Cepsilon_0%7D%5Cfrac%7B%283%5Ctimes%2010%5E%7B-6%7D%29%28-2%5Ctimes%2010%5E%7B-6%7D%29%7D%7B%280.36%29%5E2%7D%20%3D%20-0.41~N)
The minus sign in front of the force means that the force is attractive.
The direction of the force can be calculated as follows:
![F_x = F\cos(\theta)\\F_y = F\sin(\theta)](https://tex.z-dn.net/?f=F_x%20%3D%20F%5Ccos%28%5Ctheta%29%5C%5CF_y%20%3D%20F%5Csin%28%5Ctheta%29)
where θ is the angle between F and the x-axis. This angle can be calculated by the triangle with edges 0.3 m, 0.2 m, and 0.36 m.
So, sin(θ) = 0.2/0.36 = 0.55 and cos(θ) = 0.3/0.36 = 0.83.
Finally,
![F_x = -0.41 \times 0.83 = -0.34~N\\F_y = -0.41 \times 0.55 = -0.22~N](https://tex.z-dn.net/?f=F_x%20%3D%20-0.41%20%5Ctimes%200.83%20%3D%20-0.34~N%5C%5CF_y%20%3D%20-0.41%20%5Ctimes%200.55%20%3D%20-0.22~N)
Answer:
All object changes are compared with a <em>reference</em> , which is an object that appears to stay in place.
Explanation:
In scientific experiments, the changes in the experimental object are observed by comparing the changes with a reference object. In the reference object, no changes are made and conditions are kept normal in it. For example, if we want to measure the distance of two cars from a point, the point will be the reference point from which the distance shall be measured. Hence, all changes are made by comparison from a reference object or point.
Answer:
The ratio of moment of inertia of larger sphere to that of smaller sphere = 4
Explanation:
The moment of inertia of solid sphere is given by I = 2/5MR² where M = mass of sphere and R = radius of sphere.
Radius of smaller sphere = D/2
Radius of larger sphere = 2D/2 = D.
Moment of inertia of smaller sphere I₁ = 2/5M × D²/4 = MD²/10
Moment of inertia of larger sphere I₂ = 2/5M × D² = 2MD²/5
The ratio of moment of inertia of larger sphere to that of smaller sphere = I₂/I₁ = 2MD²/5 ÷ MD²/10 = 10 × 2/5 = 4