Question

Как направлено ускорение самолета,если на него действует 4 силы:сила тяжести 200 кН и подъемная сила 210 кН по вертикали; по горизонтали:сила тяги мотора 20 кН и сила лобового сопротивления воздуха 10 кН. Чему равна равнодействующая всех сил?Подробное решение.

Answer 1

Ускорение направлено под углом 45гр вверх по ходу движения самолета
Равнодействующая равна $\sqrt{10^{2}+10^{2}}$ = 14 кН

Answer 2

Calculation of the Resultant Force

To determine the resultant force acting on the airplane, we need to consider the forces acting in both the vertical and horizontal directions.

In the vertical direction, the forces acting on the airplane are the gravitational force (weight) and the lift force. The gravitational force is given as 200 kN, and the lift force is given as 210 kN. The gravitational force acts downward, while the lift force acts upward.

In the horizontal direction, the forces acting on the airplane are the thrust force from the engine and the drag force (air resistance). The thrust force is given as 20 kN, and the drag force is given as 10 kN. The thrust force acts in the direction of motion, while the drag force acts opposite to the direction of motion.

To find the resultant force, we can use vector addition. We add the forces acting in the same direction and subtract the forces acting in opposite directions.

Let's calculate the resultant force in both the vertical and horizontal directions separately.

Resultant Force in the Vertical Direction

The resultant force in the vertical direction is the difference between the gravitational force and the lift force. Since the lift force acts upward, we subtract it from the gravitational force:

Resultant force in the vertical direction = Gravitational force - Lift force

Resultant force in the vertical direction = 200 kN - 210 kN

Resultant force in the vertical direction = -10 kN

The negative sign indicates that the resultant force in the vertical direction is directed downward.

Resultant Force in the Horizontal Direction

The resultant force in the horizontal direction is the difference between the thrust force and the drag force. Since the drag force acts opposite to the direction of motion, we subtract it from the thrust force:

Resultant force in the horizontal direction = Thrust force - Drag force

Resultant force in the horizontal direction = 20 kN - 10 kN

Resultant force in the horizontal direction = 10 kN

The resultant force in the horizontal direction is directed in the direction of motion.

Resultant Force

To find the magnitude and direction of the resultant force, we can use the Pythagorean theorem and trigonometry. The magnitude of the resultant force is given by the square root of the sum of the squares of the vertical and horizontal resultant forces:

Magnitude of the resultant force = sqrt((Resultant force in the vertical direction)^2 + (Resultant force in the horizontal direction)^2)

Magnitude of the resultant force = sqrt((-10 kN)^2 + (10 kN)^2)

Magnitude of the resultant force = sqrt(100 kN^2 + 100 kN^2)

Magnitude of the resultant force = sqrt(200 kN^2)

Magnitude of the resultant force = 14.14 kN

The direction of the resultant force can be found using trigonometry. The angle between the resultant force and the horizontal direction can be calculated as:

Angle = arctan((Resultant force in the vertical direction) / (Resultant force in the horizontal direction))

Angle = arctan((-10 kN) / (10 kN))

Angle = arctan(-1)

Angle = -45 degrees

Therefore, the magnitude of the resultant force is 14.14 kN, and the direction of the resultant force is 45 degrees downward from the horizontal direction.

Summary

The resultant force acting on the airplane is 14.14 kN directed 45 degrees downward from the horizontal direction.

Please note that the calculations provided are based on the given information and assumptions.