Answer:
all of those are pisitions
Explanation:
Answer:
The hollow cylinder rolled up the inclined plane by 1.91 m
Explanation:
From the principle of conservation of mechanical energy, total kinetic energy = total potential energy
![M.E_T = \frac{1}{2}mv^2 + \frac{1}{2} I \omega^2 + mgh](https://tex.z-dn.net/?f=M.E_T%20%3D%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20I%20%5Comega%5E2%20%2B%20mgh)
The total energy at the bottom of the inclined plane = total energy at the top of the inclined plane.
![\frac{1}{2}mv_i^2 + \frac{1}{2} I \omega_i^2 + mg(0) = \frac{1}{2}mv_f^2 + \frac{1}{2} I \omega_f^2 + mgh](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dmv_i%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20I%20%5Comega_i%5E2%20%2B%20mg%280%29%20%3D%20%20%5Cfrac%7B1%7D%7B2%7Dmv_f%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20I%20%5Comega_f%5E2%20%2B%20mgh)
moment of inertia, I, of a hollow cylinder = ¹/₂mr²
substitute for I in the equation above;
![\frac{1}{2}mv_i^2 + \frac{1}{2} (\frac{1}{2}mr^2 \omega_i^2) = \frac{1}{2}mv_f^2 + \frac{1}{2} (\frac{1}{2}mr^2 \omega_f^2) + mgh\\\\ but \ v = r \omega\\\\\frac{1}{2}mv_i^2 + \frac{1}{2} (\frac{1}{2}m v_i^2 ) = \frac{1}{2}mv_f^2 + \frac{1}{2} (\frac{1}{2}m v_f^2) + mgh\\\\\frac{1}{2}mv_i^2 +\frac{1}{4}mv_i^2 = \frac{1}{2}mv_f^2 +\frac{1}{4}mv_f^2 +mgh\\\\\frac{3}{4}mv_i^2 = \frac{3}{4}mv_f^2 +mgh\\\\mgh = \frac{3}{4}mv_i^2 - \frac{3}{4}mv_f^2\\\\gh = \frac{3}{4}v_i^2 - \frac{3}{4}v_f^2\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dmv_i%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%28%5Cfrac%7B1%7D%7B2%7Dmr%5E2%20%20%5Comega_i%5E2%29%20%3D%20%20%5Cfrac%7B1%7D%7B2%7Dmv_f%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%28%5Cfrac%7B1%7D%7B2%7Dmr%5E2%20%20%5Comega_f%5E2%29%20%2B%20mgh%5C%5C%5C%5C%20but%20%5C%20v%20%3D%20r%20%5Comega%5C%5C%5C%5C%5Cfrac%7B1%7D%7B2%7Dmv_i%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%28%5Cfrac%7B1%7D%7B2%7Dm%20v_i%5E2%20%20%29%20%3D%20%20%5Cfrac%7B1%7D%7B2%7Dmv_f%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%28%5Cfrac%7B1%7D%7B2%7Dm%20v_f%5E2%29%20%2B%20mgh%5C%5C%5C%5C%5Cfrac%7B1%7D%7B2%7Dmv_i%5E2%20%2B%5Cfrac%7B1%7D%7B4%7Dmv_i%5E2%20%3D%20%5Cfrac%7B1%7D%7B2%7Dmv_f%5E2%20%2B%5Cfrac%7B1%7D%7B4%7Dmv_f%5E2%20%2Bmgh%5C%5C%5C%5C%5Cfrac%7B3%7D%7B4%7Dmv_i%5E2%20%3D%20%5Cfrac%7B3%7D%7B4%7Dmv_f%5E2%20%2Bmgh%5C%5C%5C%5Cmgh%20%3D%20%5Cfrac%7B3%7D%7B4%7Dmv_i%5E2%20-%20%20%5Cfrac%7B3%7D%7B4%7Dmv_f%5E2%5C%5C%5C%5Cgh%20%3D%20%5Cfrac%7B3%7D%7B4%7Dv_i%5E2%20-%20%20%5Cfrac%7B3%7D%7B4%7Dv_f%5E2%5C%5C%5C%5C)
![h = \frac{3}{4g}(v_1^2 -v_f^2)](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B3%7D%7B4g%7D%28v_1%5E2%20-v_f%5E2%29)
given;
v₁ = 5.0 m/s
vf = 0
g = 9.8 m/s²
![h = \frac{3}{4g}(v_1^2 -v_f^2) =\frac{3}{4*9.8}(5^2 -0) = 1.91 \ m](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B3%7D%7B4g%7D%28v_1%5E2%20-v_f%5E2%29%20%3D%5Cfrac%7B3%7D%7B4%2A9.8%7D%285%5E2%20-0%29%20%3D%201.91%20%5C%20m)
Therefore, the hollow cylinder rolled up the inclined plane by 1.91 m
Answer:
993.52 Hz
Explanation:
The frequency of sound emitted by the stationery train is 1057 Hz.
The car travels away from the train at 20.6 m/s.
The frequency the observer hears is given by the formula:
![f_o = \frac{v - v_o}{v}f](https://tex.z-dn.net/?f=f_o%20%3D%20%5Cfrac%7Bv%20-%20v_o%7D%7Bv%7Df)
where v = velocity of sound = 343 m/s
vo = velocity of observer
f = frequency from source
This phenomenon is known as Doppler's effect.
Therefore:
![f_o = \frac{343 - 20.6}{343} * 1057\\ \\f_o = 322.4 / 343 * 1057\\\\f_o = 993.52 Hz](https://tex.z-dn.net/?f=f_o%20%3D%20%5Cfrac%7B343%20-%2020.6%7D%7B343%7D%20%2A%201057%5C%5C%20%5C%5Cf_o%20%3D%20322.4%20%2F%20343%20%2A%201057%5C%5C%5C%5Cf_o%20%3D%20993.52%20Hz)
The frequency heard by the observer is 993.52 Hz.
Answer:
cần cung cấp 70 độ vì nước sôi ở 100°C
Explanation:
Answer:
Block A has the greatest density.
Explaination:
Block A density:0.0625 kg/cm3
Block B density:0.020833 kg/cm3
Block C density:0.041667 kg/cm3