Answer:
Velocity
Explanation:
Objects in motion usually have a speed which is scalar or velocity which is a vector.
A scalar quantity is one with magnitude but has no directional attribute.
A vector quantity is one with both magnitude and directional attribute.
Speed is a scalar quantity that describes the magnitude of motion a body accrues.
Velocity is a vector quantity that describes both the magnitude of motion and the direction of motion in a body.
Answer:
a). M = 20.392 kg
b). am = 0.56 
(block), aM = 0.28 (bucket)
Explanation:
a). We got N = mg cos θ,
f = 
= 
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
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
.....................(iv)
We got, N = mg cos θ
∴ 
................(v)
Mg - 2T = M
(from equation (iv))
.....................(vi)
Putting (vi) in equation (v),
![$\frac{g\left[\frac{M}{2}-m \sin \theta-\mu_K m \cos \theta\right]}{(\frac{M}{4}+m)}=a_m$](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)
Using equation (iv), we get,
The Net Force would be 2 N to the left.
21 N is being used to push the box to the right and 23 N is used to push it left. There is a stronger force pushing the box towards the left. The different in the two numbers would give you the net force acting on the box and the direction of the arrow with the greatest force will tell you the direction.
