Answer:
a = 12 [m/s²]
Explanation:
To solve this problem we must use Newton's second law which tells us that the sum of forces on a body is equal to the product of mass by acceleration.
ΣF = m*a
where:
ΣF = sum of forces acting on a body [N] (units of Newtons)
m = mass = 0.5 [kg]
a = acceleration [m/s²]
Let's take the direction of positive forces to the right and negative forces directed to the left
2 + 8 - 4 = 0.5*a
6 = 0.5*a
a = 12 [m/s²]
I'm not sure about the magnitude, but the direction of the normal force is upward.
Answer:
The torque about the origin is 
Explanation:
Torque 
is the cross product between force 
and vector position 
respect a fixed point (in our case the origin):
There are multiple ways to calculate a cross product but we're going to use most common method, finding the determinant of the matrix:
![\overrightarrow{r}\times\overrightarrow{F} =-\left[\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k}\\ F1_{x} & F1_{y} & F1_{z}\\ r_{x} & r_{y} & r_{z}\end{array}\right]](https://tex.z-dn.net/?f=%20%5Coverrightarrow%7Br%7D%5Ctimes%5Coverrightarrow%7BF%7D%20%3D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20%5Chat%7Bi%7D%20%26%20%5Chat%7Bj%7D%20%26%20%5Chat%7Bk%7D%5C%5C%20F1_%7Bx%7D%20%26%20F1_%7By%7D%20%26%20F1_%7Bz%7D%5C%5C%20r_%7Bx%7D%20%26%20r_%7By%7D%20%26%20r_%7Bz%7D%5Cend%7Barray%7D%5Cright%5D%20)
