The time of motion of ball A before they collide is 5.1 seconds.
<h3>
Time of motion</h3>
The two balls will collide at a time "t" when they attain a certain height "h".
<h3>The equation of motion</h3>
The equation of motion of the two balls is given as follows;
<em />
<em>when they collide;</em>
- A would have traveled, (t + 4) seconds
- B would have traveled t seconds
![h_A = 30(t+ 4) - \frac{1}{2} g(t+ 4)^2\\\\h_B = 30t - \frac{1}{2} gt^2](https://tex.z-dn.net/?f=h_A%20%3D%2030%28t%2B%204%29%20-%20%5Cfrac%7B1%7D%7B2%7D%20g%28t%2B%204%29%5E2%5C%5C%5C%5Ch_B%20%3D%2030t%20-%20%5Cfrac%7B1%7D%7B2%7D%20gt%5E2)
![h_B = h_A\\\\30t - \frac{1}{2} gt^2 = 30(t + 4) - \frac{1}{2} g(t + 4)^2\\\\30t - \frac{1}{2} gt^2 = 30t + 120- \frac{1}{2}gt^2- 4gt -8g\\\\0 = 120 -4gt -8g\\\\4gt +8g = 120\\\\4(9.8)t + 8(9.8) = 120\\\\39.2t + 78.4 = 120\\\\39.2 t = 41.6\\\\t = \frac{41.6}{39.2} \\\\t = 1.1 \ s](https://tex.z-dn.net/?f=h_B%20%3D%20h_A%5C%5C%5C%5C30t%20-%20%5Cfrac%7B1%7D%7B2%7D%20gt%5E2%20%3D%2030%28t%20%2B%204%29%20-%20%5Cfrac%7B1%7D%7B2%7D%20g%28t%20%2B%204%29%5E2%5C%5C%5C%5C30t%20-%20%5Cfrac%7B1%7D%7B2%7D%20gt%5E2%20%3D%2030t%20%2B%20120-%20%5Cfrac%7B1%7D%7B2%7Dgt%5E2-%204gt%20-8g%5C%5C%5C%5C0%20%3D%20120%20-4gt%20-8g%5C%5C%5C%5C4gt%20%2B8g%20%3D%20120%5C%5C%5C%5C4%289.8%29t%20%2B%208%289.8%29%20%3D%20120%5C%5C%5C%5C39.2t%20%2B%2078.4%20%3D%20120%5C%5C%5C%5C39.2%20t%20%3D%2041.6%5C%5C%5C%5Ct%20%3D%20%5Cfrac%7B41.6%7D%7B39.2%7D%20%5C%5C%5C%5Ct%20%3D%201.1%20%5C%20s)
Thus, the time of motion of ball A before they collide is (1.1 + 4) = 5.1 seconds.
Learn more about time of motion here: brainly.com/question/2364404
Answer:
275 MPa, -175 MPa
-0.63636
450 MPa
Explanation:
= Maximum stress
= Minimum stress
= Mean stress = 50 MPa
= Stress amplitude = 225 MPa
Mean stress is given by
![\sigma_m=\frac{\sigma_{max}+\sigma_{min}}{2}\\\Rightarrow \sigma_{max}+\sigma_{min}=2\sigma_m\\\Rightarrow \sigma_{max}+\sigma_{min}=2\times 50\\\Rightarrow \sigma_{max}+\sigma_{min}=100\ MPa\\\Rightarrow \sigma_{max}=100-\sigma_{min}](https://tex.z-dn.net/?f=%5Csigma_m%3D%5Cfrac%7B%5Csigma_%7Bmax%7D%2B%5Csigma_%7Bmin%7D%7D%7B2%7D%5C%5C%5CRightarrow%20%5Csigma_%7Bmax%7D%2B%5Csigma_%7Bmin%7D%3D2%5Csigma_m%5C%5C%5CRightarrow%20%5Csigma_%7Bmax%7D%2B%5Csigma_%7Bmin%7D%3D2%5Ctimes%2050%5C%5C%5CRightarrow%20%5Csigma_%7Bmax%7D%2B%5Csigma_%7Bmin%7D%3D100%5C%20MPa%5C%5C%5CRightarrow%20%5Csigma_%7Bmax%7D%3D100-%5Csigma_%7Bmin%7D)
Stress amplitude is given by
![\sigma_a=\frac{\sigma_{max}-\sigma_{min}}{2}\\\Rightarrow \sigma_{max}-\sigma_{min}=2\sigma_a\\\Rightarrow \sigma_{max}-\sigma_{min}=2\times 225\\\Rightarrow \sigma_{max}-\sigma_{min}=450\ MPa\\\Rightarrow 100-\sigma_{min}-\sigma_{min}=450\\\Rightarrow -2\sigma_{min}=350\\\Rightarrow \sigma_{min}=-175\ MPa](https://tex.z-dn.net/?f=%5Csigma_a%3D%5Cfrac%7B%5Csigma_%7Bmax%7D-%5Csigma_%7Bmin%7D%7D%7B2%7D%5C%5C%5CRightarrow%20%5Csigma_%7Bmax%7D-%5Csigma_%7Bmin%7D%3D2%5Csigma_a%5C%5C%5CRightarrow%20%5Csigma_%7Bmax%7D-%5Csigma_%7Bmin%7D%3D2%5Ctimes%20225%5C%5C%5CRightarrow%20%5Csigma_%7Bmax%7D-%5Csigma_%7Bmin%7D%3D450%5C%20MPa%5C%5C%5CRightarrow%20100-%5Csigma_%7Bmin%7D-%5Csigma_%7Bmin%7D%3D450%5C%5C%5CRightarrow%20-2%5Csigma_%7Bmin%7D%3D350%5C%5C%5CRightarrow%20%5Csigma_%7Bmin%7D%3D-175%5C%20MPa)
![\sigma_{max}=100-\sigma_{min}\\\Rightarrow \sigma_{max}=100-(-175)\\\Rightarrow \sigma_{max}=275\ MPa](https://tex.z-dn.net/?f=%5Csigma_%7Bmax%7D%3D100-%5Csigma_%7Bmin%7D%5C%5C%5CRightarrow%20%5Csigma_%7Bmax%7D%3D100-%28-175%29%5C%5C%5CRightarrow%20%5Csigma_%7Bmax%7D%3D275%5C%20MPa)
Maximum stress level is 275 MPa
Minimum stress level is -175 MPa
Stress ratio is given by
![R=\frac{\sigma_{min}}{\sigma_{max}}\\\Rightarrow R=\frac{-175}{275}\\\Rightarrow R=-0.63636](https://tex.z-dn.net/?f=R%3D%5Cfrac%7B%5Csigma_%7Bmin%7D%7D%7B%5Csigma_%7Bmax%7D%7D%5C%5C%5CRightarrow%20R%3D%5Cfrac%7B-175%7D%7B275%7D%5C%5C%5CRightarrow%20R%3D-0.63636)
The stress ratio is -0.63636
Stress range is given by
![\sigma_{max}-\sigma_{min}=450\ MPa](https://tex.z-dn.net/?f=%5Csigma_%7Bmax%7D-%5Csigma_%7Bmin%7D%3D450%5C%20MPa)
Magnitude of the stress range is 450 MPa
Answer:
4.17 m/s²
Explanation:
We are told the reaction time is 0.2 s. Now, during this reaction time the car is going to travel an additional distance of
: x = u × t = 40 × 0.2 = 8 m
where u is the initial velocity of the car which is 40.0 m/s.
We are told that he had 200 m to stop before applying brakes. Thus, after applying brakes, he now has a distance to cover of; s = 200 - 8 = 192 m
Since vehicle is coming to rest acceleration would be negative, thus using Newton's equation of motion, we have;
v
² = u² - 2as
v = 0 m/s since it's coming to rest
u = 40 m/s
s = 192 m
Thus;
0² = 40² - 2(a)(192)
0² = 1600 - 384a
a = 1600/384
a = 4.17 m/s²
Multiplied by; speed = distance x time
Answer:
Amplitude is the vertical distance between a ridge and the midpoint of the wave.
Explanation:
A mechanical wave is a disturbance that travels through a material or substance that is a medium of the wave. For example, when a tense string is pressed, the disturbance caused spreads along it in the form of a wave pulse. The disturbance in this case consists in the variation of The Shape of the string from its equilibrium state
it is important to know:
Crest: the crest is the highest point of this amplitude.
Period: the period is the time it takes the wave to go from one point of maximum amplitude to the next.
Amplitude: amplitude is the vertical distance between a crest and the midpoint of the wave.
Frequency: number of times that vibration is repeated.
Valley: it is the lowest point of a wave.
Wavelength: distance between two consecutive ridges of this size.
Transverse wave velocity.-
The propagation speed of a wave on a string (v) is proportional to the square root of the string tension (T) and inversely proportional to the square root of the linear density (μ) of the string:
![v = \sqrt{\frac{T}{μ} }](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7BT%7D%7B%CE%BC%7D%20%7D)