Answer:
θ = 14.27°
Explanation:
The only force acting on the puck is the gravitational force. Since the track is banked with an angle θ, we have to separate the components of the weight.
For the sake of simplicity, I will denote the perpendicular direction to the truck as the y-direction, and the direction along the radius as the x-direction.
So, the free-body diagram of the puck is as follows:
1- x-component of the weight of the puck: mgsinθ
2- y-component of the weight of the puck: mgcosθ
3- Normal force in the y-direction perpendicular to the track.
Since there is no motion on the y-direction, normal force is equal to the y-component of the weight of the puck.
The x-component of the weight of the puck is equal to the centripetal force according to Newton's Second Law:
![F = ma\\mg\sin{\theta} = \frac{mv^2}{R}\\\sin{\theta} = \frac{v^2}{gR}](https://tex.z-dn.net/?f=F%20%3D%20ma%5C%5Cmg%5Csin%7B%5Ctheta%7D%20%3D%20%5Cfrac%7Bmv%5E2%7D%7BR%7D%5C%5C%5Csin%7B%5Ctheta%7D%20%3D%20%5Cfrac%7Bv%5E2%7D%7BgR%7D)
Substituting the variables given in the question, the angle of the track can be found:
![\sin{\theta} = \frac{(31.9)^2}{(9.8)(421)} = 0.2466\\\theta = 14.27^\circ](https://tex.z-dn.net/?f=%5Csin%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%2831.9%29%5E2%7D%7B%289.8%29%28421%29%7D%20%3D%200.2466%5C%5C%5Ctheta%20%3D%2014.27%5E%5Ccirc)
Explanation:
Given
Velocity v = 23.0m/s
Distance S = 3.45m
Required
Time it will take the skier to reach the ground;
Using the equation of motion;
S = ut + 1/2gt²
3.45 = 23t + 1/2(9.8)t²
3.45 = 23t + 4.9t²
4.9t²+23t-3.45 = 0
Factorize;
t = -23 ±√23²-4(4.9)(-3.45)/2(4.9)
t = -23 ±√529+67.62/9.8
t = -23±√596.62/9.8
t = -23±24.43/9.8
t = 1.43/9.8
t = 0.146 secs
Hence take the skier 0.146 secs to reach the ground.
b) Horizontal distance covered is the range;
Range = U√2H/g
Range = 23√2(3.45)/9.8
Range = 23√6.9/9.8
Range = 23√0.7041
Range = 23(0.8391)
Range = 19.29m
Hence the horizontal distance travelled in air is 19.29m
The answer is that "elements are a single atom and compounds are a mixture of two elements or more." Elements are atoms that have protons, neutrons, and electrons. Compounds are mixtures with two or more elements.
Hope this helps.
the neutrons through the nucleus?
Explanation:
Carbon cycle am pretty sure it that