Calculating Components and Magnitude of Forces and Acceleration

[jrfskater]

Homework Statement

Forces F1 and F2 act on a mass m = 0.52 kg, as shown in the diagram below.
The magnitudes of the forces and angles are as follows:
F1 = 2.2 N, θ1 = 59 degrees
F2 = 1.7 N, θ2 = 68 degrees

http://loncapa.vcu.edu/res/vcu/delewis/physics/images/Two%20Forces%20(2).jpg

Homework Equations

What are the x and y components of the force F1?
( , ) N


What are the x and y components of the force F2?
( , ) N


What are the x and y components of the sum of these two forces (the resultant force)?
( , ) N


What is the magnitude of the resultant force?
N

What are the x and y components of the resulting acceleration of the mass?
( , m/s2


What is the magnitude of the acceleration?
m/s2

The Attempt at a Solution

 

[Mindscrape]

How come everything is filled out except for 3.?

 

[Moetasim]

To calculate the x and y components of the force F1, we can use the following equations:

Fx = F1*cos(θ1)
Fy = F1*sin(θ1)

Plugging in the values given in the problem, we get:

Fx = 2.2*cos(59) = 1.1 N
Fy = 2.2*sin(59) = 1.9 N

Similarly, for force F2:

Fx = 1.7*cos(68) = 0.7 N
Fy = 1.7*sin(68) = 1.5 N

To find the x and y components of the sum of the two forces (the resultant force), we can simply add the x and y components of each force:

Rx = 1.1 + 0.7 = 1.8 N
Ry = 1.9 + 1.5 = 3.4 N

The magnitude of the resultant force can be calculated using the Pythagorean theorem:

R = √(Rx² + Ry²) = √(1.8² + 3.4²) = 3.9 N

To find the resulting acceleration of the mass, we can use Newton's second law:

ΣF = ma

Where ΣF is the sum of all the forces acting on the mass, m is the mass and a is the resulting acceleration.

In this case, the sum of the forces is the resultant force, so we can rewrite the equation as:

R = ma

Solving for a, we get:

a = R/m = 3.9/0.52 = 7.5 m/s²

Therefore, the x and y components of the resulting acceleration are (1.8 m/s², 3.4 m/s²) and the magnitude of the acceleration is 7.5 m/s².