The figure is missing: find it in attachment.
a) (3i - 5j) N
First of all, we have to write each force as a vector with a direction:
- Force F1 points downward, so along the negative y-direction, so we can write it as
- Force F2 points to the right, so along the positive x-direction, so we can write it as
- Force F3 points to the left, so along the negative x-direction, so we can write it as
Now we can write the net force, by adding the three vectors and separating the x-component from the y-component:
b) 5.8 N
The magnitude of the net force can be calculated by applying Pythagorean's theorem on the components of the net force:
where
is the x-component
is the y-component
Substituting into the equation,
c)
The angle of the net force, measured with respect to the positive x-axis (counterclockwise), can be calculated by using the formula
where
is the x-component
is the y-component
Substituting into the equation, we find
d)
The acceleration can be found by using Newton's second law:
where
F is the net force on an object
m is its mass
a is the acceleration
For the object in the problem, we know
F = 5.8 N
m = 6.9 kg
Solving the equation for a, we find the magnitude of the acceleration:
