The top row of boxes is " F O R C E " .
Hello!
a) Assuming this is asking for the minimum speed for the rock to make the full circle, we must find the minimum speed necessary for the rock to continue moving in a circular path when it's at the top of the circle.
At the top of the circle, we have:
- Force of gravity (downward)
*Although the rock is still connected to the string, if the rock is swinging at the minimum speed required, there will be no tension in the string.
Therefore, only the force of gravity produces the net centripetal force:
![\Sigma F = F_g\\\\F_c = F_g\\\\\frac{mv^2}{r} = mg](https://tex.z-dn.net/?f=%5CSigma%20F%20%3D%20F_g%5C%5C%5C%5CF_c%20%3D%20F_g%5C%5C%5C%5C%5Cfrac%7Bmv%5E2%7D%7Br%7D%20%3D%20mg)
We can simplify and rearrange the equation to solve for 'v'.
![\frac{v^2}{r} = g\\\\v^2 = gr\\\\v = \sqrt{gr}](https://tex.z-dn.net/?f=%5Cfrac%7Bv%5E2%7D%7Br%7D%20%3D%20g%5C%5C%5C%5Cv%5E2%20%3D%20gr%5C%5C%5C%5Cv%20%3D%20%5Csqrt%7Bgr%7D)
Plugging in values:
![v = \sqrt{9.8 * 0.75} = \boxed{2.711 m/s^}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B9.8%20%2A%200.75%7D%20%3D%20%5Cboxed%7B2.711%20m%2Fs%5E%7D)
b)
Let's do a summation of forces at the bottom of the swing. We have:
- Force due to gravity (downward, -)
- Tension force (upward, +)
The sum of these forces produces a centripetal force, upward (+).
![\Sigma F = T - F_g\\\\F_c = T - F_g\\\\\frac{mv^2}{r} = T - mg](https://tex.z-dn.net/?f=%5CSigma%20F%20%3D%20T%20-%20F_g%5C%5C%5C%5CF_c%20%3D%20T%20-%20F_g%5C%5C%5C%5C%5Cfrac%7Bmv%5E2%7D%7Br%7D%20%3D%20T%20-%20mg)
Rearranging for 'T":
![T = \frac{mv^2}{r} + mg\\\\](https://tex.z-dn.net/?f=T%20%3D%20%20%20%5Cfrac%7Bmv%5E2%7D%7Br%7D%20%2B%20%20mg%5C%5C%5C%5C)
Plugging in the appropriate values:
![T = \frac{(0.2)(2.711^2)}{(0.75)} + 0.2(9.8) = \boxed{3.92 N}](https://tex.z-dn.net/?f=T%20%3D%20%20%5Cfrac%7B%280.2%29%282.711%5E2%29%7D%7B%280.75%29%7D%20%2B%200.2%289.8%29%20%3D%20%5Cboxed%7B3.92%20N%7D)
By <span> It is directly proportional to the </span>average kinetic energy<span>.</span>
Answer:
a.Beth
b.2232 s
Explanation:
We are given that
Distance,d=400 mi
Speed of Alan,v=45 mph
Speed of Beth,v'=55 mph
a.Time =![\frac{distance}{speed}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%7D%7Bspeed%7D)
Using the formula
Time taken by Alan=![\frac{400}{45}=8.89 hr](https://tex.z-dn.net/?f=%5Cfrac%7B400%7D%7B45%7D%3D8.89%20hr)
Time taken by Beth=![\frac{400}{55}=7.27hr](https://tex.z-dn.net/?f=%5Cfrac%7B400%7D%7B55%7D%3D7.27hr)
Alan will reach San Francisco at 4:53 PM
Beth will reach San Francisco at 4:16 PM
Beth will reach before Alan.
b.Difference between time=8.89-7.27=1.62 hr
t=1.62 hr
1.62-1=0.62 hr
0.62 hr=![0.62\times 60\times 60=2232 s](https://tex.z-dn.net/?f=0.62%5Ctimes%2060%5Ctimes%2060%3D2232%20s)
Hence, Beth has to wait 2232 s for Alan to arrive .
Answer:
(4) The physical and chemical properties of these minerals determine how humans use them.
Explanation:
All the materials and the metals found on earth shows certain characteristics naturally or in their physical state. These physical characteristics can be their look, their structure, their color, strength, melting point, boiling point, density, etc.
And chemical properties of the metals are defined as those characteristics or features of the metals that it exhibits when these metals reacts chemically.
The physical properties as well as the chemical properties distinguishes each metal from each other. These properties determines how people use these metals in their life.