Question

Two forces are acting on an object. One force has a magnitude of 45 N and is directed along the + 𝑥 axis. The other force has a magnitude of 30 N and is directed along the + 𝑦 axis. What is the direction of the object’s acceleration? Express your answer by giving the angle between 𝑎 → and the 𝑥 axis.

Answer 1

To find the direction of the object's acceleration, we need to calculate the net force acting on the object and then calculate the angle between the net force vector and the x-axis.

Given:
First force magnitude (F1) = 45 N along the +x axis
Second force magnitude (F2) = 30 N along the +y axis

To find the net force, we need to find the x and y components of each force.

For F1 along the x-axis:
F1x = F1 * cos(0)
F1x = 45 * cos(0)
F1x = 45

For F2 along the y-axis:
F2y = F2 * cos(90)
F2y = 30 * cos(90)
F2y = 0

The net force along the x-axis:
Fx = F1x + F2x
Fx = 45 + 0
Fx = 45 N

The net force along the y-axis:
Fy = F2y + F2y
Fy = 0 + 30
Fy = 30 N

The magnitude of the net force:
Fnet = sqrt(Fx^2 + Fy^2)
Fnet = sqrt(45^2 + 30^2)
Fnet = sqrt(2025 + 900)
Fnet = sqrt(2925)
Fnet ≈ 54 N

The angle between the net force vector and the x-axis can be calculated as:
tanθ = Fy / Fx
tanθ = 30 / 45
θ = arctan(30 / 45)
θ ≈ arctan(2/3)
θ ≈ 33.69 degrees

Therefore, the direction of the object's acceleration is at an angle of approximately 33.69 degrees with the x-axis.