Answer:
The magnitude of the acceleration is ![a_r = 1.50 \ m/s^2](https://tex.z-dn.net/?f=a_r%20%3D%201.50%20%5C%20m%2Fs%5E2)
The direction is
north of east
Explanation:
From the question we are told that
The force exerted by the wind is ![F_{sail} = (330 ) \ N \ north](https://tex.z-dn.net/?f=F_%7Bsail%7D%20%3D%20%20%28330%20%29%20%5C%20N%20%5C%20north)
The force exerted by water is ![F_{keel} = (210 ) \ N \ east](https://tex.z-dn.net/?f=F_%7Bkeel%7D%20%3D%20%20%28210%20%20%29%20%5C%20N%20%5C%20east)
The mass of the boat(+ crew) is
Now Force is mathematically represented as
![F = ma](https://tex.z-dn.net/?f=F%20%3D%20%20ma)
Now the acceleration towards the north is mathematically represented as
![a_n = \frac{F_{sail}}{m_b}](https://tex.z-dn.net/?f=a_n%20%20%3D%20%20%5Cfrac%7BF_%7Bsail%7D%7D%7Bm_b%7D)
substituting values
![a_n = \frac{330 }{260}](https://tex.z-dn.net/?f=a_n%20%20%3D%20%20%5Cfrac%7B330%20%7D%7B260%7D)
![a_n = 1.269 \ m/s^2](https://tex.z-dn.net/?f=a_n%20%20%3D%20%201.269%20%5C%20m%2Fs%5E2)
Now the acceleration towards the east is mathematically represented as
![a_e = \frac{F_{keel}}{m_b }](https://tex.z-dn.net/?f=a_e%20%3D%20%5Cfrac%7BF_%7Bkeel%7D%7D%7Bm_b%20%7D)
substituting values
![a_e = \frac{210}{260}](https://tex.z-dn.net/?f=a_e%20%3D%20%5Cfrac%7B210%7D%7B260%7D)
![a_e =0.808 \ m/s^2](https://tex.z-dn.net/?f=a_e%20%3D0.808%20%5C%20m%2Fs%5E2)
The resultant acceleration is
![a_r = \sqrt{a_e^2 + a_n^2}](https://tex.z-dn.net/?f=a_r%20%3D%20%20%5Csqrt%7Ba_e%5E2%20%2B%20a_n%5E2%7D)
substituting values
![a_r = \sqrt{(0.808)^2 + (1.269)^2}](https://tex.z-dn.net/?f=a_r%20%3D%20%20%5Csqrt%7B%280.808%29%5E2%20%2B%20%281.269%29%5E2%7D)
![a_r = 1.50 \ m/s^2](https://tex.z-dn.net/?f=a_r%20%3D%201.50%20%5C%20m%2Fs%5E2)
The direction with reference from the north is evaluated as
Apply SOHCAHTOA
![tan \theta = \frac{a_e}{a_n}](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%3D%20%20%5Cfrac%7Ba_e%7D%7Ba_n%7D)
![\theta = tan ^{-1} [\frac{a_e}{a_n } ]](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%20%5E%7B-1%7D%20%5B%5Cfrac%7Ba_e%7D%7Ba_n%20%7D%20%5D)
substituting values
![\theta = tan ^{-1} [\frac{0.808}{1.269 } ]](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%20%5E%7B-1%7D%20%5B%5Cfrac%7B0.808%7D%7B1.269%20%7D%20%5D)
![\theta = tan ^{-1} [0.636 ]](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%20%5E%7B-1%7D%20%5B0.636%20%5D)
![\theta = 32.5 6^o](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%2032.5%206%5Eo)
Answer: 0.5N
Explanation: if the system is at equilibrium, sum of the torque will be equal to zero.
But if they are not in equilibrium.
U will find the difference in the two torque
find the attached file for solution
Answer:
Explanation:
The radius of the smaller bubble, r1 will decrease and that of the bigger bubble, r2 will increase.
The pressure that is present in the smaller bubble usually is greater than the pressure that exists inside that of the bigger bubble. This then makes air to flow from r1 to r2 thereby making the radius of the smaller bubble r1, to decrease while keeping that of the bigger bubble r2 higher.
Answer:
(A). The speed of the ions is ![1.2\times10^{6}\ m/s](https://tex.z-dn.net/?f=1.2%5Ctimes10%5E%7B6%7D%5C%20m%2Fs)
(B). The radius of curvature of a singly charged lithium ion is ![2.0\times10^{6}\ m](https://tex.z-dn.net/?f=2.0%5Ctimes10%5E%7B6%7D%5C%20m)
Explanation:
Given that,
Electric field = 60000 N/C
Magnetic field = 0.0500 T
(A). We need to calculate the velocity
For no deflection
![F_{E}=F_{B}](https://tex.z-dn.net/?f=F_%7BE%7D%3DF_%7BB%7D)
![Eq=Bqv](https://tex.z-dn.net/?f=Eq%3DBqv)
![v = \dfrac{E}{B}](https://tex.z-dn.net/?f=v%20%3D%20%5Cdfrac%7BE%7D%7BB%7D)
![v=\dfrac{60000}{0.0500}](https://tex.z-dn.net/?f=v%3D%5Cdfrac%7B60000%7D%7B0.0500%7D)
![v=1.2\times10^{6}\ m/s](https://tex.z-dn.net/?f=v%3D1.2%5Ctimes10%5E%7B6%7D%5C%20m%2Fs)
(B). We need to calculate the radius
Using magnetic force balance by centripetal force
![Bqv=\dfrac{mv^2}{r}](https://tex.z-dn.net/?f=Bqv%3D%5Cdfrac%7Bmv%5E2%7D%7Br%7D)
![r=\dfrac{mv^2}{Bqv}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Bmv%5E2%7D%7BBqv%7D)
Put the value into the formula
![r=\dfrac{1.16\times10^{-26}\times(1.2\times10^{6})^2}{0.0500\times1.6\times10^{-19}}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7B1.16%5Ctimes10%5E%7B-26%7D%5Ctimes%281.2%5Ctimes10%5E%7B6%7D%29%5E2%7D%7B0.0500%5Ctimes1.6%5Ctimes10%5E%7B-19%7D%7D)
![r=2.0\times10^{6}\ m](https://tex.z-dn.net/?f=r%3D2.0%5Ctimes10%5E%7B6%7D%5C%20m)
Hence, (A). The speed of the ions is ![1.2\times10^{6}\ m/s](https://tex.z-dn.net/?f=1.2%5Ctimes10%5E%7B6%7D%5C%20m%2Fs)
(B). The radius of curvature of a singly charged lithium ion is ![2.0\times10^{6}\ m](https://tex.z-dn.net/?f=2.0%5Ctimes10%5E%7B6%7D%5C%20m)
Answer: 1100 ft lb/s and 2 H.P
Explanation:
To calculate for the power developed in the elevator motor in ft.lb/s, we multiply the distance and the weight of the elevator and divide the product by the time.
Power = (10 ft)(2200 lb) / 20 s = 1100 ft.lb/s
Next, convert the calculated value to HP.
1100 ft.lb/s x (1 HP/ 550 ft.lb/s) = 2 HP
hope this helps please give brainliest!