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 90°-0- M Block 6 (b) Frictionless (a) F, sin 8 Fcos 6 Fsin 8 (c)

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### Problem Description

Refer to the figure. Let the mass of the block be 5.90 kg and the angle \( \theta \) be 29.0°. 

1. **(a)** Find the tension in the cord.
2. **(b)** Find the normal force acting on the block.
3. **(c)** If the cord is cut, find the magnitude of the block's acceleration.

### Diagram Description

#### Diagram (a)
This is a side view schematic diagram showing a block of mass \( m \) resting on a frictionless inclined plane. The angle of inclination is \( \theta \). A cord is attached to the block and supports it as it lies against a vertical wall.

#### Diagram (b)
A free-body diagram showing the forces acting on the block:

- \( \vec{F}_{N} \): The normal force acting perpendicular to the surface of the incline.
- \( \vec{T} \): The tension in the cord acting towards the top of the incline.
- \( \vec{F}_{g} \): The gravitational force acting vertically downward.
- Angles and components are marked, showing \( 90° - \theta \) and the angle \( \theta \).

#### Diagram (c)
A coordinate system is depicted with axes \( x \) and \( y \), breaking down the gravitational force \( \vec{F}_{g} \) into components:

- \( F_{g} \sin \theta \): The component of gravitational force parallel to the incline.
- \( F_{g} \cos \theta \): The component of gravitational force perpendicular to the incline.

This explanation and diagrams help in understanding how to calculate the tension in the cord, normal force, and subsequent acceleration when the cord is cut.
Transcribed Image Text:### Problem Description Refer to the figure. Let the mass of the block be 5.90 kg and the angle \( \theta \) be 29.0°. 1. **(a)** Find the tension in the cord. 2. **(b)** Find the normal force acting on the block. 3. **(c)** If the cord is cut, find the magnitude of the block's acceleration. ### Diagram Description #### Diagram (a) This is a side view schematic diagram showing a block of mass \( m \) resting on a frictionless inclined plane. The angle of inclination is \( \theta \). A cord is attached to the block and supports it as it lies against a vertical wall. #### Diagram (b) A free-body diagram showing the forces acting on the block: - \( \vec{F}_{N} \): The normal force acting perpendicular to the surface of the incline. - \( \vec{T} \): The tension in the cord acting towards the top of the incline. - \( \vec{F}_{g} \): The gravitational force acting vertically downward. - Angles and components are marked, showing \( 90° - \theta \) and the angle \( \theta \). #### Diagram (c) A coordinate system is depicted with axes \( x \) and \( y \), breaking down the gravitational force \( \vec{F}_{g} \) into components: - \( F_{g} \sin \theta \): The component of gravitational force parallel to the incline. - \( F_{g} \cos \theta \): The component of gravitational force perpendicular to the incline. This explanation and diagrams help in understanding how to calculate the tension in the cord, normal force, and subsequent acceleration when the cord is cut.
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