Two forces are acting on air craft of mass 200kg as shown figures 600N north and 200N east
. What is the acceleration of the aircraft?
The acceleration of the aircraft can be calculated using Newton's Second Law of Motion, which states that the acceleration of an object is equal to the net force divided by the mass of the object. In this case, the net force is 400N (600N - 200N) and the mass is 200kg, so the acceleration of the aircraft is 2 m/s^2.
To find the resultant force of two forces acting on an aircraft, we can use vector addition. Given that one force of 600N is acting north and another force of 200N is acting east, we can treat these forces as perpendicular components of a right triangle.
Step 1: Draw a diagram representing the forces.
```
|
| 600N (north)
|
-----O----- 200N (east)
|
|
```
Step 2: Resolve the forces into their components.
The force of 600N acting north can be resolved into vertical component V and the force of 200N acting east can be resolved into the horizontal component H.
```
|
| V (vertical)
|
--->O----- H (horizontal)
|
|
```
Step 3: Calculate the vertical and horizontal components.
The vertical component (V) is equal to the force acting north, which is 600N.
V = 600N
The horizontal component (H) is equal to the force acting east, which is 200N.
H = 200N
Step 4: Find the resultant force.
To find the resultant force, we can use the Pythagorean theorem.
Resultant force (R) = √(V² + H²)
R = √(600N² + 200N²)
= √(360,000N² + 40,000N²)
= √(400,000N²)
= 632.455N (rounded to three decimal places)
Step 5: Find the direction of the resultant force.
To find the direction of the resultant force, we can use trigonometry. The angle (θ) between the resultant force and the horizontal axis can be found using the inverse tangent function.
θ = tan^(-1)(V / H)
θ = tan^(-1)(600N / 200N)
= tan^(-1)(3)
≈ 71.565 degrees (rounded to three decimal places)
Therefore, the resultant force acting on the aircraft is approximately 632.455N at an angle of 71.565 degrees from the horizontal axis.