Understanding the Forces

* Gravity (Weight): The block experiences a downward force due to gravity, which we call its weight (mg, where 'm' is the mass and 'g' is the acceleration due to gravity).

* Normal Force: The inclined plane pushes back on the block perpendicular to the surface, creating a normal force.

* Tension: The string pulls on the block, creating tension.

Free Body Diagram

Draw a free body diagram of the block. This is a visual representation of all the forces acting on the block.

* Draw the block on the inclined plane.

* Draw an arrow pointing straight down from the block to represent the force of gravity (mg).

* Draw an arrow perpendicular to the inclined plane, pointing away from the block, to represent the normal force (N).

* Draw an arrow parallel to the inclined plane, pointing upwards, to represent the tension force (T).

Resolving Forces

Since the block is motionless (in equilibrium), the forces must balance. We need to resolve the forces into components parallel and perpendicular to the inclined plane:

* Parallel to the Inclined Plane:

* Gravity has a component parallel to the plane: mg * sin(theta), where theta is the angle of the incline.

* Tension acts directly in this direction.

* Perpendicular to the Inclined Plane:

* Gravity has a component perpendicular to the plane: mg * cos(theta).

* The normal force balances this component.

Applying Newton's Laws

* Newton's First Law: An object at rest will stay at rest unless acted upon by a net force. Since the block is motionless, the net force acting on it in both directions (parallel and perpendicular to the plane) must be zero.

* Parallel to the Plane: The forces are tension (T) upwards and the component of gravity downwards (mg * sin(theta)). Since these must balance:

* T = mg * sin(theta)

Conclusion

The magnitude of the tension in the string is equal to the component of the block's weight that is acting parallel to the inclined plane. This can be calculated as:

T = mg * sin(theta)

Where:

* T is the tension in the string

* m is the mass of the block

* g is the acceleration due to gravity (approximately 9.8 m/s²)

* theta is the angle of the incline