Answer:
The tension in the cord is ![T=\frac{MR^{2}g }{2b^{2}+R^{2} }](https://tex.z-dn.net/?f=T%3D%5Cfrac%7BMR%5E%7B2%7Dg%20%7D%7B2b%5E%7B2%7D%2BR%5E%7B2%7D%20%20%7D)
Explanation:
Given:
M = mass
b = radius
R = spool of radius
The equation is:
(eq. 1)
The sum of forces in y:
∑Fy = Mg - T = Ma
![Mg=(M+\frac{MR^{2} }{2b^{2} } )a\\a=\frac{2b^{2}g }{2b^{2}+R^{2} }](https://tex.z-dn.net/?f=Mg%3D%28M%2B%5Cfrac%7BMR%5E%7B2%7D%20%7D%7B2b%5E%7B2%7D%20%7D%20%20%29a%5C%5Ca%3D%5Cfrac%7B2b%5E%7B2%7Dg%20%7D%7B2b%5E%7B2%7D%2BR%5E%7B2%7D%20%20%7D)
Replacing in eq. 1
![T=\frac{MR^{2} }{2b^{2} } (\frac{2b^{2}g }{2b^{2} +R^{2} } )\\T=\frac{MR^{2}g }{2b^{2}+R^{2} }](https://tex.z-dn.net/?f=T%3D%5Cfrac%7BMR%5E%7B2%7D%20%7D%7B2b%5E%7B2%7D%20%7D%20%28%5Cfrac%7B2b%5E%7B2%7Dg%20%7D%7B2b%5E%7B2%7D%20%2BR%5E%7B2%7D%20%7D%20%29%5C%5CT%3D%5Cfrac%7BMR%5E%7B2%7Dg%20%7D%7B2b%5E%7B2%7D%2BR%5E%7B2%7D%20%20%7D)
Answer:
The answer is "Choice E".
Explanation:
In this situation the option e is right because its resistance decreases through time, however, the time is the same for the same reason, whereas the sphere deteriorates, somehow it travels shorter distances however if the air resistance becomes are using the amplitude of movement declines, that's why other choices were wrong.
166x5.75= 954.5 meters in 5.75 seconds.
Answer:
meteorite is a piece of interplanetary debris that lives its fiery drops during a through the earth's atmosphere and strikes the surface of the earth.
Explanation:
the meteorites which are most useful for the determination of the age of the solar system are the primitive meteorites. they consist light of colored or grey silicates mixed with metallic grains. the parent bodies of these meteorites are also mostly believed to be pieces asteriods left after they formed in the solar system.
Answer:
The resultant velocity is <u>169.71 km/h at angle of 45° measured clockwise with the x-axis</u> or the east-west line.
Explanation:
Considering west direction along negative x-axis and north direction along positive y-axis
Given:
The car travels at a speed of 120 km/h in the west direction.
The car then travels at the same speed in the north direction.
Now, considering the given directions, the velocities are given as:
Velocity in west direction is, ![\overrightarrow{v_1}=-120\ \vec{i}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_1%7D%3D-120%5C%20%5Cvec%7Bi%7D)
Velocity in north direction is, ![\overrightarrow{v_2}=120\ \vec{j}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_2%7D%3D120%5C%20%5Cvec%7Bj%7D)
Now, since
are perpendicular to each other, their resultant magnitude is given as:
![|\overrightarrow{v_{res}}|=\sqrt{|\overrightarrow{v_1}|^2+|\overrightarrow{v_2}|^2}](https://tex.z-dn.net/?f=%7C%5Coverrightarrow%7Bv_%7Bres%7D%7D%7C%3D%5Csqrt%7B%7C%5Coverrightarrow%7Bv_1%7D%7C%5E2%2B%7C%5Coverrightarrow%7Bv_2%7D%7C%5E2%7D)
Plug in the given values and solve for the magnitude of the resultant.This gives,
![|\overrightarrow{v_{res}}|=\sqrt{(120)^2+(120)^2}\\\\|\overrightarrow{v_{res}}|=120\sqrt{2} = 169.71\ km/h](https://tex.z-dn.net/?f=%7C%5Coverrightarrow%7Bv_%7Bres%7D%7D%7C%3D%5Csqrt%7B%28120%29%5E2%2B%28120%29%5E2%7D%5C%5C%5C%5C%7C%5Coverrightarrow%7Bv_%7Bres%7D%7D%7C%3D120%5Csqrt%7B2%7D%20%3D%20169.71%5C%20km%2Fh)
Let the angle made by the resultant be 'x' degree with the east-west line or the x-axis.
So, the direction is given as:
![x=\tan^{-1}(\frac{|v_2|}{|v_1|})\\\\x=\tan^{-1}(\frac{120}{-120})=\tan^{-1}(-1)=-45\ deg(clockwise\ angle\ with\ the\ x-axis)](https://tex.z-dn.net/?f=x%3D%5Ctan%5E%7B-1%7D%28%5Cfrac%7B%7Cv_2%7C%7D%7B%7Cv_1%7C%7D%29%5C%5C%5C%5Cx%3D%5Ctan%5E%7B-1%7D%28%5Cfrac%7B120%7D%7B-120%7D%29%3D%5Ctan%5E%7B-1%7D%28-1%29%3D-45%5C%20deg%28clockwise%5C%20angle%5C%20with%5C%20the%5C%20x-axis%29)
Therefore, the resultant velocity is 169.71 km/h at angle of 45° measured clockwise with the x-axis or the east-west line.