Two forces are applied to a car in an effort to accelerate it, as shown below. The first force, F1 = 364 N, is applied at an angle α = 33° to the forward dashed line. The second force, F2 = 522 N, is applied at an angle β = 11° to the forward dashed line.

Question

Two forces are applied to a car in an effort to accelerate it, as shown below. The first force, F1 = 364 N, is applied at an angle α = 33° to the forward dashed line. The second force, F2 = 522 N, is applied at an angle β = 11° to the forward dashed line.
What is the resultant of these two forces?
in N and at what degree
If the car has a mass of 3050 kg, what acceleration does it have? (Disregard friction.)
in m/s2 at what degree

Jennifer · Answer

Take components of the force:

F1x = 364*cos(33)
F1y = 364*sin(33)

F2x = 522*cos(11)
F2y = 522*sin(11)

Fnetx = F1x + F2x
Fnety = F1y + F2y

Fnet = ((Fnetx)^2 + (Fnety)^2)^0.5

at an angle theta given by

tan(theta) = Fnety/Fnetx

where Fnet = m*a = 3050*a

Solve for a, the acceleration