Equations of the vertical launch:
Vf = Vo - gt
y = yo + Vo*t - gt^2 / 2
Here yo = 35.0m
Vo is unknown
y final = 0
t = 4.00 s
and I will approximate g to 10m/s^2
=> 0 = 35.0 + Vo * 4 - 5 * (4.00)^2 => Vo = [-35 + 5*16] / 4 = - 45 / 4 = -11.25 m/s
The negative sign is due to the fact that the initial velocity is upwards and we assumed that the direction downwards was positive when used g = 10m/s^2.
Answer: 11.25 m/s
The load is the weight of the rock that Jonathan lifts:
![L=3000 N](https://tex.z-dn.net/?f=L%3D3000%20N)
The effort instead is the force applied in input to the lever in order to lift the rock:
![E=300 N](https://tex.z-dn.net/?f=E%3D300%20N)
So, the ratio between load and effort for this exercise is
![\frac{L}{E}= \frac{3000 N}{300 N}=10](https://tex.z-dn.net/?f=%20%5Cfrac%7BL%7D%7BE%7D%3D%20%5Cfrac%7B3000%20N%7D%7B300%20N%7D%3D10%20%20)
So, the ratio is 10:1.
Answer:
![q=1\times10^{-8}C](https://tex.z-dn.net/?f=q%3D1%5Ctimes10%5E%7B-8%7DC)
Explanation:
Let the charge on the ball bearing is q.
charge on glass bead, Q = 20 nC = 20 x 10^-9 C
Force between them, F = 0.018 N
Distance between them, d = 1 cm = 0.01 m
By use of Coulomb's law in electrostatics
![F=\frac{KQq}{d^{2}}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7BKQq%7D%7Bd%5E%7B2%7D%7D)
By substituting the values
![0.018=\frac{9\times10^{9}\times20\times10^{-9}q}{0.01^{2}}](https://tex.z-dn.net/?f=0.018%3D%5Cfrac%7B9%5Ctimes10%5E%7B9%7D%5Ctimes20%5Ctimes10%5E%7B-9%7Dq%7D%7B0.01%5E%7B2%7D%7D)
![q=1\times10^{-8}C](https://tex.z-dn.net/?f=q%3D1%5Ctimes10%5E%7B-8%7DC)
Thus, the charge on the ball bearing is ![q=1\times10^{-8}C](https://tex.z-dn.net/?f=q%3D1%5Ctimes10%5E%7B-8%7DC)
Answer:
![\mu=0.0049Kg/m](https://tex.z-dn.net/?f=%5Cmu%3D0.0049Kg%2Fm)
Explanation:
When a standing wave is formed with six loops means the normal mode of the wave is n=6, the frequency of the normal mode is given by the expression:
![f_n=\frac{nv}{2L}](https://tex.z-dn.net/?f=f_n%3D%5Cfrac%7Bnv%7D%7B2L%7D)
Where
is the length of the string and
the velocity of propagation. Use this expression to find the value of
.
![f_6=\frac{6v}{2L}\\(150)=\frac{6v}{2(2)} \\150=\frac{3v}{2} \\3v=150(2)\\ v=\frac{300}{3} \\v=100m/s](https://tex.z-dn.net/?f=f_6%3D%5Cfrac%7B6v%7D%7B2L%7D%5C%5C%28150%29%3D%5Cfrac%7B6v%7D%7B2%282%29%7D%20%5C%5C150%3D%5Cfrac%7B3v%7D%7B2%7D%20%5C%5C3v%3D150%282%29%5C%5C%20v%3D%5Cfrac%7B300%7D%7B3%7D%20%5C%5Cv%3D100m%2Fs)
The velocity of propagation is given by the expression:
![v=\sqrt{\frac{T}{\mu }](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7BT%7D%7B%5Cmu%20%7D)
Where
is the desirable variable of the problem, the linear mass density, and
is the tension of the cord. The tension is equal to the weight of the mass hanging from the cord:
![T=W=mg=(5)(9.81)=49.05N](https://tex.z-dn.net/?f=T%3DW%3Dmg%3D%285%29%289.81%29%3D49.05N)
With the value of the tension and the velocity you can find the mass density:
![v=\sqrt{\frac{T}{\mu}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7BT%7D%7B%5Cmu%7D)
![v^2=\frac{T}{\mu}\\ \mu=\frac{T}{v^2} =\frac{49.05}{(100)^2} =\frac{49.05}{10000} =0.0049Kg/m](https://tex.z-dn.net/?f=v%5E2%3D%5Cfrac%7BT%7D%7B%5Cmu%7D%5C%5C%20%5Cmu%3D%5Cfrac%7BT%7D%7Bv%5E2%7D%20%3D%5Cfrac%7B49.05%7D%7B%28100%29%5E2%7D%20%3D%5Cfrac%7B49.05%7D%7B10000%7D%20%3D0.0049Kg%2Fm)