Answer:
b) Vertical= 144.15N [up]
horizontal= 61.19N [right]
c) -61.19N [Left]
D) 9.8m - 144.15 = Fn
Explanation:
a) to draw the free body diagram, you would draw a square to represent the object, being the cart. The forces acting on it are Force of gravity (Fg going down), Normal force (Fn going up), Force applied (Fa going up right), and Force of friction (Ff,going to the left, opposite of Fa).
b) So the applied force is 156.6N, and has an angle of 67. the 156.6N is the hypotenuse, so you would need to find the opposite side (vertical component), and adjacent side (horizontal component):
vertical:
sinθ = opp / hyp
sin67 = opp / 156.6
opp = 144.15N [up]
horizontal:
cosθ = adj / hyp
cos67 = adj / 156.6
adj = 61.19N [right]
c)Since the cart has constant velocity, the acceleration is 0, meaning no net force (fnet = ma, a = 0, fnet = 0), so the horizontal component of the applied force is equal to the frictional force. Heres why mathematically. (X DIRECTION ) :
Fnet = Fa + Ff
0 = Fa + Ff
-Ff = Fa.
So the force of friction has the same magnitude, but opposite direction. So since the horizontal component of applied force was 61.19 N, the frictional force will be -61.19N
d) So now we are looking at the Fnet in the y direction, which is also 0 because the car is remaining on the ground, its not going up nor down:
Fnety = 0
Fnet is composed of Fg, Fn and Fay (force applied in y direction);
fnet = Fn + Fay + Fg. Fn and Fay are both up, and Fg is down, so u need to subtract Fg:
fnet = Fn + Fay - Fg.
0 = Fn + 144.15 - mg
mg - 144.15 = Fn
9.8m - 144.15 = Fn
Since it didnt give you a mass thats how much you could simplify it down to, in order to get the Fn
