Two forces, 395 N at 11◦
and 344 N at 34◦
are
applied to a car in an effort to accelerate it.
(3049 kg is the car)
What is the magnitude of the resultant of
these two forces?
Answer in units of N.
Fx = 395 cos 11 + 344 cos 34
Fy = 395 sin 11 + 344 sin 34
|F| = sqrt (Fx^2 + Fy^2)
To find the magnitude of the resultant of these two forces, we can use the concept of vector addition. The resultant force can be calculated by adding the individual forces as vectors.
First, let's break down the given forces into their horizontal and vertical components.
Force 1:
Magnitude: 395 N
Angle: 11 degrees
Force 2:
Magnitude: 344 N
Angle: 34 degrees
To find the horizontal and vertical components of each force, we can use trigonometric functions. The horizontal component can be calculated by multiplying the magnitude of the force by the cosine of the angle, and the vertical component can be calculated by multiplying the magnitude of the force by the sine of the angle.
Force 1:
Horizontal component: 395 N * cos(11 degrees)
Vertical component: 395 N * sin(11 degrees)
Force 2:
Horizontal component: 344 N * cos(34 degrees)
Vertical component: 344 N * sin(34 degrees)
Now that we have the horizontal and vertical components of each force, we can add them together to find the resultant force.
Horizontal component of the resultant force = Sum of the horizontal components of the individual forces
Vertical component of the resultant force = Sum of the vertical components of the individual forces
Finally, we can use Pythagoras' theorem to find the magnitude of the resultant force. The magnitude of a vector is given by the square root of the sum of the squares of its components.
Magnitude of the resultant force = sqrt((Horizontal component of the resultant force)^2 + (Vertical component of the resultant force)^2)
Now let's plug in the values and calculate the magnitude of the resultant force.