The missile’s engine exerts a 260-kN force F.Express F in terms of components using the coordinate system shown.The mass of the missile is 8800 kg. Determine the magnitude of the sum of the forces exerted by the engine and the missile’s weight. The image depicts a missile launch graphically represented on a Cartesian coordinate system. ### Description:1. **Coordinate Axes**: - The horizontal axis is labeled as the x-axis. - The vertical axis is labeled as the y-axis.2. **Missile Path**: - The missile is shown ascending at an angle. - The missile’s movement can be divided into horizontal and vertical components.3. **Right Triangle Formation**: - To the right of the missile, a right triangle is formed with sides labeled as 3 and 4, representing the vertical and horizontal components of the missile's movement respectively. - The hypotenuse of this right triangle, labeled as F, represents the actual path or distance traveled by the missile.### Explanation of Graph:The graph visually represents the path of a missile launch demonstrating vector components in physics. - The horizontal distance (x-component) is '4' units.- The vertical height (y-component) is '3' units.- The hypotenuse 'F' can be calculated using the Pythagorean theorem, \( F = \sqrt{3^2 + 4^2} \).This representation is commonly used to demonstrate vector decomposition, which is the process of breaking down a vector into its orthogonal components. ### Educational Significance:Understanding this graphical representation helps students grasp fundamental concepts in physics, particularly in the study of vectors and motion. Through such visual aids, complex topics such as projectile motion and force decomposition become more intuitive and easier to comprehend. ### Inclined Plane and ForcesThis image shows a diagram of an inclined plane used to illustrate the forces acting on an object placed on the incline. The coordinate axes are labeled \(x\) (horizontal) and \(y\) (vertical).#### Components of the Diagram:- **Inclined Plane:** A right triangle is depicted, representing the inclined plane. The base of the triangle measures 4 units horizontally across the \(x\)-axis. The vertical height from the base to the top of the incline is 3 units along the \(y\)-axis. - **Hypotenuse:** The hypotenuse of the right triangle represents the slope of the inclined plane.- **Force \(F\):** An arrow labeled \(F\) is drawn along the hypotenuse of the triangle, indicating the direction of the force acting along the inclined plane. This force is often the result of a push or pull that keeps the object moving along the incline.- **Weight \(W\):** A vertical arrow labeled \(W\) points downward from the object, representing the force of gravity acting on the object. #### Forces on an Inclined Plane:- The inclined plane demonstrates the resolution of forces when an object rests or slides down an incline. The force of gravity \(W\) acts directly downward.- The force \(F\), which could be a component of gravity or another applied force, acts along the plane of the incline.#### Applications:Understanding inclined planes is crucial in physics and engineering for analyzing the motion of objects, calculating the work done by forces, and solving problems related to angles and force components.### Summary:This diagram helps students visualize the physical scenario of forces acting on an inclined plane and assists in understanding the resolution of gravitational force into components parallel and perpendicular to the inclined surface.

The given figure is shown below:

The missile’s engine exerts a 260-kN force F. Express F in terms of components using the coordinate system shown. The mass of the missile is 8800 kg. Determine the magnitude of the sum of the forces exerted by the engine and the missile’s weight.

The missile’s engine exerts a 260-kN force F. Express F in terms of components using the coordinate system shown. The mass of the missile is 8800 kg. Determine the magnitude of the sum of the forces exerted by the engine and the missile’s weight.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

The missile’s engine exerts a 260-kN force F.

Express F in terms of components using the coordinate system shown.
The mass of the missile is 8800 kg. Determine the magnitude of the sum of the forces exerted by the engine and the missile’s weight.

The image depicts a missile launch graphically represented on a Cartesian coordinate system.

### Description:

1. **Coordinate Axes**:
- The horizontal axis is labeled as the x-axis.
- The vertical axis is labeled as the y-axis.

2. **Missile Path**:
- The missile is shown ascending at an angle.
- The missile’s movement can be divided into horizontal and vertical components.

3. **Right Triangle Formation**:
- To the right of the missile, a right triangle is formed with sides labeled as 3 and 4, representing the vertical and horizontal components of the missile's movement respectively.
- The hypotenuse of this right triangle, labeled as F, represents the actual path or distance traveled by the missile.

### Explanation of Graph:

The graph visually represents the path of a missile launch demonstrating vector components in physics.
- The horizontal distance (x-component) is '4' units.
- The vertical height (y-component) is '3' units.
- The hypotenuse 'F' can be calculated using the Pythagorean theorem, \( F = \sqrt{3^2 + 4^2} \).

This representation is commonly used to demonstrate vector decomposition, which is the process of breaking down a vector into its orthogonal components.

### Educational Significance:

Understanding this graphical representation helps students grasp fundamental concepts in physics, particularly in the study of vectors and motion. Through such visual aids, complex topics such as projectile motion and force decomposition become more intuitive and easier to comprehend.

### Inclined Plane and Forces

This image shows a diagram of an inclined plane used to illustrate the forces acting on an object placed on the incline. The coordinate axes are labeled \(x\) (horizontal) and \(y\) (vertical).

#### Components of the Diagram:

- **Inclined Plane:**
A right triangle is depicted, representing the inclined plane. The base of the triangle measures 4 units horizontally across the \(x\)-axis. The vertical height from the base to the top of the incline is 3 units along the \(y\)-axis.

- **Hypotenuse:**
The hypotenuse of the right triangle represents the slope of the inclined plane.

- **Force \(F\):**
An arrow labeled \(F\) is drawn along the hypotenuse of the triangle, indicating the direction of the force acting along the inclined plane. This force is often the result of a push or pull that keeps the object moving along the incline.

- **Weight \(W\):**
A vertical arrow labeled \(W\) points downward from the object, representing the force of gravity acting on the object.

#### Forces on an Inclined Plane:

- The inclined plane demonstrates the resolution of forces when an object rests or slides down an incline. The force of gravity \(W\) acts directly downward.
- The force \(F\), which could be a component of gravity or another applied force, acts along the plane of the incline.

#### Applications:

Understanding inclined planes is crucial in physics and engineering for analyzing the motion of objects, calculating the work done by forces, and solving problems related to angles and force components.

### Summary:

This diagram helps students visualize the physical scenario of forces acting on an inclined plane and assists in understanding the resolution of gravitational force into components parallel and perpendicular to the inclined surface.

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