Answer:
15
Explanation:
mass, M = 5Kg
horizontal force, F_h = 40N
acceleration, a =5 m/s^2
frictional force, F_f =?
net force = ma
net force = F_h - F_f = 40N - F_f
40 - F_f = 5 x 5
- F_f = 25 - 40
multiply both side by -1
F_f = 40 - 25 = 15
the frictional force is 15N
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
They attract and stick together