There are two forces acting on an object. One force has a magnitude of 35 N and is directed along the +x axis. The other force has a magnitude of 20 N and is directed along the +y axis. What is the direction of the acceleration of the object? Express your answer by giving the angle between vector a and the x axis.
To find the direction of the acceleration of the object, we can use vector addition.
Step 1: Represent each force as a vector. The force along the +x axis can be represented as F1 = 35 N in the +x direction. The force along the +y axis can be represented as F2 = 20 N in the +y direction.
Step 2: Add the two force vectors together. We can do this by summing their components. The x component of the acceleration can be found by adding the x components of the force vectors, while the y component of the acceleration can be found by adding the y components of the force vectors.
Ax = F1x + F2x = 35 N + 0 N = 35 N
Ay = F1y + F2y = 0 N + 20 N = 20 N
Step 3: Use the components of acceleration to find the magnitude and direction. The magnitude of the acceleration can be found using the Pythagorean theorem:
|a| = sqrt(Ax^2 + Ay^2) = sqrt((35 N)^2 + (20 N)^2) = sqrt(1225 N^2 + 400 N^2) = sqrt(1625 N^2) ≈ 40.31 N
To find the direction of the acceleration, we can use trigonometry. The angle between the acceleration vector and the x axis can be found using the inverse tangent function:
θ = arctan(Ay / Ax) = arctan(20 N / 35 N)
Calculating this will give us the angle in radians. To convert it to degrees, we can use the conversion factor of 180°/π radians.
Let's calculate the angle:
θ = arctan(20 N / 35 N) ≈ 29.74°
Therefore, the direction of the acceleration of the object is approximately 29.74° relative to the x axis.