Statika Partikel 3D (2/5): Contoh Soal Komponen Gaya dalam Tiga Dimensi

Summary

The video explains a physics problem where a hot air balloon is tethered to a car by a rope with a known tension of 800 N. The task is to calculate the force components of the rope in Cartesian coordinates. The force is resolved into X, Y, and Z components based on given angles. Through the application of trigonometric functions like sine and cosine, the force is decomposed, and the Cartesian components of the force vector are determined. The final result is a vector representation of the force in three dimensions, providing a clear solution to the problem.

Takeaways

• 😀 The problem involves a hot air balloon tied to a car with ropes, and the goal is to determine the components of the force vector in Cartesian coordinates.
• 😀 Three key points are involved: point O (tie to the car), point A (projection on the ground), and point B (tie to the balloon).
• 😀 The coordinate system is defined with the X-axis horizontal, the Y-axis vertical, and the Z-axis perpendicular to the XY plane.
• 😀 The angle between the force vector and the Z-axis is given as 60°.
• 😀 Trigonometric functions like sine and cosine are used to break down the force into components along the X, Y, and Z axes.
• 😀 The tension in the rope is given as 800 N, and the force is projected along the axes using angles.
• 😀 The component of the force in the X direction is calculated using sine and cosine of 45° and 60°.
• 😀 The component of the force in the Z direction is calculated by using cosine with an angle of 60°.
• 😀 The final components of the force vector in Cartesian coordinates are: 489.90 N along the X-axis, 565.69 N along the Y-axis, and 282.85 N along the Z-axis.
• 😀 The importance of proper labeling and understanding of the system's angles and projections is emphasized to solve the problem correctly.
• 😀 It is crucial to remember to write the units (N for Newtons) when expressing the components of the force.

Q & A

What is the primary topic of the script?

The script describes a physics problem involving tension in a rope connected to a balloon and a car. It aims to resolve the force vector into its Cartesian components.

What is the tension in the rope as given in the problem?

The tension in the rope is 800 N.

What are the three key points mentioned in the problem setup?

The three key points are: point O (the attachment on the car), point A (a vertical projection from point B), and point B (the attachment on the balloon).

How are the coordinates of the system defined in the problem?

The system is defined in a 3D coordinate system with the X-axis, Y-axis, and Z-axis, with a specific explanation of how the axes are oriented (e.g., Z-axis is vertical and X-axis is horizontal).

What angle is given between the Z-axis and the rope in the problem?

The angle between the Z-axis and the rope (line OA) is 60°.

What trigonometric functions are used to resolve the force vector into components?

The script uses the sine (sin) and cosine (cos) functions to break down the force vector into its components along the X, Y, and Z axes.

How do the components of the force (FB) relate to the angle of 45°?

Since the angle between the force and the line OA is 45°, the components FB (along the X and Z axes) are calculated using the sine and cosine of 45°.

What is the force value obtained after applying trigonometry for FB?

The value of FB after applying the sine and cosine of 45° is 565.69 N.

What is the resulting force component along the X-axis (Fx)?

The force component along the X-axis (Fx) is 489.90 N.

What is the force component along the Z-axis (Fz)?

The force component along the Z-axis (Fz) is 282.85 N.

Why is it important to break the force vector into components in this problem?

Breaking the force vector into components allows for a clearer understanding of how the force is distributed along the X, Y, and Z axes, making it easier to solve for specific forces and determine the effect of the tension in the system.