answer:
resultant = 127.65 in the positive direction
explanation:
F1 = 50N , F2 = 40N, f3 = 55N , f4 = 60N
Fy = 50 sin 50 = 50 × -0.26 = -13
Fx = 40 cos 0 = 40×1 = 40
fx = 55 cos 25 = 55×0.99 = 54.45
Fy = 60 sin 70 = 60 × 0.77 = 46.2
resultant = -13+40+54.45+46.2 = 127.65 in the positive direction
Some call it "air resistance", and others just call it "drag".
Answer:
The kinetic energy of the mass at the instant it passes back through the equilibrium position is 0.06500 J.
Explanation:
Given that,
Mass = 2.15 kg
Distance = 0.0895 m
Amplitude = 0.0235 m
We need to calculate the spring constant
Using newton's second law
![F= mg](https://tex.z-dn.net/?f=F%3D%20mg)
Where, f = restoring force
![kx=mg](https://tex.z-dn.net/?f=kx%3Dmg)
![k=\dfrac{mg}{x}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7Bmg%7D%7Bx%7D)
Put the value into the formula
![k=\dfrac{2.15\times9.8}{0.0895}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B2.15%5Ctimes9.8%7D%7B0.0895%7D)
![k=235.41\ N/m](https://tex.z-dn.net/?f=k%3D235.41%5C%20N%2Fm)
We need to calculate the kinetic energy of the mass
Using formula of kinetic energy
![K.E=\dfrac{1}{2}mv^2](https://tex.z-dn.net/?f=K.E%3D%5Cdfrac%7B1%7D%7B2%7Dmv%5E2)
Here, ![v = A\omega](https://tex.z-dn.net/?f=v%20%3D%20A%5Comega)
![K.E=\dfrac{1}{2}m\times(A\omega)^2](https://tex.z-dn.net/?f=K.E%3D%5Cdfrac%7B1%7D%7B2%7Dm%5Ctimes%28A%5Comega%29%5E2)
Here, ![\omega=\sqrt{\dfrac{k}{m}}^2](https://tex.z-dn.net/?f=%5Comega%3D%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D%5E2)
![K.E=\dfrac{1}{2}m\times A^2\sqrt{\dfrac{k}{m}}^2](https://tex.z-dn.net/?f=K.E%3D%5Cdfrac%7B1%7D%7B2%7Dm%5Ctimes%20A%5E2%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D%5E2)
![K.E=\dfrac{1}{2}kA^2](https://tex.z-dn.net/?f=K.E%3D%5Cdfrac%7B1%7D%7B2%7DkA%5E2)
Put the value into the formula
![K.E=\dfrac{1}{2}\times235.41\times(0.0235)^2](https://tex.z-dn.net/?f=K.E%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes235.41%5Ctimes%280.0235%29%5E2)
![K.E=0.06500\ J](https://tex.z-dn.net/?f=K.E%3D0.06500%5C%20J)
Hence, The kinetic energy of the mass at the instant it passes back through the equilibrium position is 0.06500 J.
The Greek philosopher Aristotle and the Roman Catholic Church also believed the sun revolved around the earth. In 1543, Nicolaus Copernicus<span> published a new theory stating the earth revolves around the sun. This is known as the Copernican theory.</span>