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A 1.60 kg box rests on a plank that is inclined at an angle of 55.0° above the horizontal. The upper end of the box isattached to a spring with a force constant of 21.0 N/m, as shown in the figure. If the coefficient of static friction betweenthe box and the plank is 0.15, what is the maximum amount the spring can be stretched and the box remain at rest?

A 1.60 kg box rests on a plank that is inclined at an angle of 55.0° above the horizontal. The upper end of the box isattached to a spring with a force constant of 21.0 N/m, as shown in the figure. If the coefficient of static friction betweenthe box and the plank is 0.15, what is the maximum amount the spring can be stretched and the box remain at rest?

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A 1.60 kg box rests on a plank that is inclined at an angle of 55.0° above the horizontal. The upper end of the box isattached to a spring with a force constant of 21.0 N/m, as shown in the figure. If the coefficient of static friction betweenthe box and the plank is 0.15, what is the maximum amount the spring can be stretched and the box remain at rest?

 

 

**Diagram Explanation:** The image illustrates a physical scenario involving a block, an incline, and a spring. Here's a detailed breakdown: - **Inclined Plane:** A light green inclined surface is shown, indicating an angle θ with the horizontal. This angle is crucial for calculating components of forces acting parallel and perpendicular to the incline. - **Block:** A purple square block rests on the incline. This block is subject to gravitational force, normal force from the incline, and spring force due to contact with the spring. - **Spring:** Attached at the upper part of the incline, the spring is shown in a compressed state against the block. The spring will exert a force proportional to its compression according to Hooke's Law (F = -kx), where k is the spring constant and x is the compression distance. This setup is commonly used in physics to study energy transformations, such as potential energy conversion to kinetic energy, and to evaluate force interactions. It is also useful for understanding concepts like friction, motion on inclined planes, and harmonic motion.
Transcribed Image Text:**Diagram Explanation:** The image illustrates a physical scenario involving a block, an incline, and a spring. Here's a detailed breakdown: - **Inclined Plane:** A light green inclined surface is shown, indicating an angle θ with the horizontal. This angle is crucial for calculating components of forces acting parallel and perpendicular to the incline. - **Block:** A purple square block rests on the incline. This block is subject to gravitational force, normal force from the incline, and spring force due to contact with the spring. - **Spring:** Attached at the upper part of the incline, the spring is shown in a compressed state against the block. The spring will exert a force proportional to its compression according to Hooke's Law (F = -kx), where k is the spring constant and x is the compression distance. This setup is commonly used in physics to study energy transformations, such as potential energy conversion to kinetic energy, and to evaluate force interactions. It is also useful for understanding concepts like friction, motion on inclined planes, and harmonic motion.
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