**Physics Problem: Block on an Inclined Plane****Problem Statement:**Refer to the figure. Let the mass of the block be 5.90 kg and the angle θ be 29.0°. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the magnitude of the block's acceleration.**Diagrams:**- **Figure (a):** - A block of mass $ m $ is placed on an inclined plane with an angle of θ to the horizontal. - The incline is labeled as frictionless. - A cord is attached to the block, preventing it from sliding down the plane.- **Figure (b):** (Free Body Diagram - Block on Incline) - A coordinate system is established, with the x-axis along the incline and the y-axis perpendicular to it. - Forces acting on the block: - $ \vec{F}_N $ (Normal Force): Perpendicular to the inclined surface. - $ \vec{T} $ (Tension): Up the incline. - $ \vec{F}_g $ (Gravitational Force): Acting vertically downward. - Angle $ 90° - θ $ is marked between the vertical and the normal force.- **Figure (c):** (Resolution of Forces) - Gravitational force $ \vec{F}_g $ is resolved into components: - $ F_g \sin θ $: Component parallel to the incline. - $ F_g \cos θ $: Component perpendicular to the incline. - The block's weight acts downwards and is decomposed into these components in the x and y directions as defined by the inclined plane's coordinate system.This setup allows you to apply Newton's laws to solve for tension, normal force, and acceleration.

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Refer to the figure. Let the mass of the block be 5.90 kg and the angle 8 be 29.0°. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the magnitude of the block's acceleration. 0 m Frictionless 3

Refer to the figure. Let the mass of the block be 5.90 kg and the angle 8 be 29.0°. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the magnitude of the block's acceleration. 0 m Frictionless 3

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter5: More Applications Of Newton’s Laws

Section: Chapter Questions

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Newton’s Third Law of Motion

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”

Question

**Physics Problem: Block on an Inclined Plane**

**Problem Statement:**
Refer to the figure. Let the mass of the block be 5.90 kg and the angle θ be 29.0°. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the magnitude of the block's acceleration.

**Diagrams:**

- **Figure (a):**
- A block of mass $ m $ is placed on an inclined plane with an angle of θ to the horizontal.
- The incline is labeled as frictionless.
- A cord is attached to the block, preventing it from sliding down the plane.

- **Figure (b):** (Free Body Diagram - Block on Incline)
- A coordinate system is established, with the x-axis along the incline and the y-axis perpendicular to it.
- Forces acting on the block:
- $ \vec{F}_N $ (Normal Force): Perpendicular to the inclined surface.
- $ \vec{T} $ (Tension): Up the incline.
- $ \vec{F}_g $ (Gravitational Force): Acting vertically downward.
- Angle $ 90° - θ $ is marked between the vertical and the normal force.

- **Figure (c):** (Resolution of Forces)
- Gravitational force $ \vec{F}_g $ is resolved into components:
- $ F_g \sin θ $: Component parallel to the incline.
- $ F_g \cos θ $: Component perpendicular to the incline.
- The block's weight acts downwards and is decomposed into these components in the x and y directions as defined by the inclined plane's coordinate system.

This setup allows you to apply Newton's laws to solve for tension, normal force, and acceleration.

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