Final answer:
To find the acceleration and final velocity of the block, we have to convert the acting force to the horizontal, then find the friction force. Subtracting the friction from the horizontal force gives us the net force. The acceleration of the block is found by dividing the net force by the mass of the block, and the final velocity is given by multiplying the acceleration by the time period.
Step-by-step explanation:
The first step is to find out the horizontal force that is actually acting on the block (Since the force is at an angle). Only the horizontal component of this force contributes to the block's horizontal motion. The horizontal component of the force (F) is 30N*cos(50) = 19.32N.
The frictional force (Ff) is equal to the coefficient of kinetic friction times the weight of the block. This comes out to be: Ff = μ*m*g = (1/8)*4*9.81 = 4.905N.
Now we can calculate the net force acting on the block by subtracting the friction from the horizontal force. This gives us: Fnet = F - Ff = 19.32N - 4.905N = 14.415N.
(a) Now, the acceleration of the block (a) is given by Newton's second law: Fnet = m*a, so a = Fnet / m = 14.415 / 4 = 3.60 m/s^2.
(b) The final velocity (Vf) of the block is given by the equation Vf = Vi + a*t. However, the block starts from rest, so Vi = 0 and the time travelled (t) is found by pace equation: d = vi*t + 0.5*a*t^2 => t = sqrt(2d/a)= sqrt(2*2/3.604) = 0.85 s. Substituting these into the former equation gives: Vf = 3.604 * 0.85 = 3.06 m/s.
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