C- Incentives it’s like a reward ~!
Temperature - The measure of the average kinetic energy of a substance
Internal Energy - Total potential and kinetic energies of the particles of a substance
Heat - Thermal energy that flows from one substance to another
Thermal Energy - Part of internal energy that can be transferred
A good way for me to remember things is to study it, and to write it down! Say you want the formula for speed, I would write the formula multiple times on a piece of paper!
Here's a video that I haven't actually watched, I just looked it up! It might help you out though: <span>https://www.youtube.com/watch?v=-Wqrw4G79Kc</span>
Answer:
a). M = 20.392 kg
b). am = 0.56
(block), aM = 0.28
(bucket)
Explanation:
a). We got N = mg cos θ,
f = ![$\mu_s N$](https://tex.z-dn.net/?f=%24%5Cmu_s%20N%24)
= ![$\mu_s mg \cos \theta$](https://tex.z-dn.net/?f=%24%5Cmu_s%20mg%20%5Ccos%20%5Ctheta%24)
If the block is ready to slide,
T = mg sin θ + f
T = mg sin θ +
.....(i)
2T = Mg ..........(ii)
Putting (ii) in (i), we get
![$\frac{Mg}{2}=mg \sin \theta + \mu_s mg \sin \theta$](https://tex.z-dn.net/?f=%24%5Cfrac%7BMg%7D%7B2%7D%3Dmg%20%5Csin%20%5Ctheta%20%2B%20%5Cmu_s%20mg%20%5Csin%20%5Ctheta%24)
![$M=2(m \sin \theta + \mu_s mg \cos \theta)$](https://tex.z-dn.net/?f=%24M%3D2%28m%20%5Csin%20%5Ctheta%20%2B%20%5Cmu_s%20mg%20%5Ccos%20%5Ctheta%29%24)
![$M=2 \times 10 \times (\sin 30^\circ+0.6 \cos 30^\circ)$](https://tex.z-dn.net/?f=%24M%3D2%20%5Ctimes%2010%20%5Ctimes%20%28%5Csin%2030%5E%5Ccirc%2B0.6%20%5Ccos%2030%5E%5Ccirc%29%24)
M = 20.392 kg
b).
.............(iii)
Here, l = total string length
Differentiating equation (iii) double time w.r.t t, l, h and h' are constants, so
![$-\ddot{x}-2\ddot x_M=0$](https://tex.z-dn.net/?f=%24-%5Cddot%7Bx%7D-2%5Cddot%20x_M%3D0%24)
![$\ddot x_M=\frac{\ddot x_m}{2}$](https://tex.z-dn.net/?f=%24%5Cddot%20x_M%3D%5Cfrac%7B%5Cddot%20x_m%7D%7B2%7D%24)
.....................(iv)
We got, N = mg cos θ
![$f_K=\mu_K mg \cos \theta$](https://tex.z-dn.net/?f=%24f_K%3D%5Cmu_K%20mg%20%5Ccos%20%5Ctheta%24)
∴ ![$T-(mg \sin \theta + f_K) = ma_m$](https://tex.z-dn.net/?f=%24T-%28mg%20%5Csin%20%5Ctheta%20%2B%20f_K%29%20%3D%20ma_m%24)
................(v)
Mg - 2T = M![a_M](https://tex.z-dn.net/?f=a_M)
![$Mg-Ma_M=2T$](https://tex.z-dn.net/?f=%24Mg-Ma_M%3D2T%24)
(from equation (iv))
.....................(vi)
Putting (vi) in equation (v),
![$\frac{Mg}{2}-\frac{Ma_M}{4}-mf \sin \theta-\mu_K mg \cos \theta = ma_m$](https://tex.z-dn.net/?f=%24%5Cfrac%7BMg%7D%7B2%7D-%5Cfrac%7BMa_M%7D%7B4%7D-mf%20%5Csin%20%5Ctheta-%5Cmu_K%20mg%20%5Ccos%20%5Ctheta%20%3D%20ma_m%24)
![$\frac{g\left[\frac{M}{2}-m \sin \theta-\mu_K m \cos \theta\right]}{(\frac{M}{4}+m)}=a_m$](https://tex.z-dn.net/?f=%24%5Cfrac%7Bg%5Cleft%5B%5Cfrac%7BM%7D%7B2%7D-m%20%5Csin%20%5Ctheta-%5Cmu_K%20m%20%5Ccos%20%5Ctheta%5Cright%5D%7D%7B%28%5Cfrac%7BM%7D%7B4%7D%2Bm%29%7D%3Da_m%24)
![$\frac{9.8\left[\frac{20.392}{2}-10(\sin 30+0.5 \cos 30)\right]}{(\frac{20.392}{4}+10)}=a_m$](https://tex.z-dn.net/?f=%24%5Cfrac%7B9.8%5Cleft%5B%5Cfrac%7B20.392%7D%7B2%7D-10%28%5Csin%2030%2B0.5%20%5Ccos%2030%29%5Cright%5D%7D%7B%28%5Cfrac%7B20.392%7D%7B4%7D%2B10%29%7D%3Da_m%24)
![$a_m= 0.56 \ m/s^2$](https://tex.z-dn.net/?f=%24a_m%3D%200.56%20%5C%20m%2Fs%5E2%24)
Using equation (iv), we get,
![a_M= 0.28 \ m/s^2](https://tex.z-dn.net/?f=a_M%3D%200.28%20%5C%20m%2Fs%5E2)
Answer:
the skater is falling bc of gravity and kinetic energy
Explanation: