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Gravity is one of the fundamental forces that plays a key role in this problem. It is the force that pulls objects toward the Earth. When describing gravity in physics, it usually refers to the gravitational force acting on an object, which is the object's weight. The weight of an object can be calculated by the formula:

• Weight, or gravitational force, is given by: \( F_{gravity} = mg \)

Here, \( m \) stands for the mass of the object, and \( g \) is the acceleration due to gravity, approximately \( 9.8 \, \text{m/s}^2 \) on Earth.
In the context of a tilted bed, gravity causes the patient to exert a force on the bed both downward and parallel to its surface. When you tilt the bed, gravity works to make the patient slide down because it has two components:

• Parallel to the surface: \( mg \sin\theta \)
• Perpendicular to the surface: \( mg \cos\theta \)

Understanding these components is crucial for solving how the bed's angle influences when sliding starts.

Normal force is the force exerted by a surface perpendicular to an object resting on it. It is essential to balance the forces acting on an object to prevent it from falling through or sinking into the surface.
In the case of a patient on a tilted bed, the normal force acts perpendicular to the plane of the bed. It counterbalances the component of gravity that is perpendicular to the bed’s surface:

• Normal force \( N = mg \, \cos\theta \)

The normal force adjusts according to the angle of the bed, influencing how much static friction is available to keep the patient from sliding. Since friction depends on the normal force (\( f = \mu_s N \)), understanding how \( N \) varies with \( \theta \) is crucial in determining the conditions for "no-sliding." The greater the normal force, the more frictional force is available to counteract the sliding motion.

A tilted bed is a simple yet intriguing example of physics at work, presenting us with the situation where static friction is put to the test. When the bed is tilted at an angle \( \theta \), the balance between gravity and friction determines whether the patient will slide or remain in place.
As the bed’s angle increases, so does the gravitational component trying to make the patient slide down (\( mg \sin\theta \)). At the same time, the normal force that's directed perpendicular to the bed’s surface decreases, leading to a lower frictional force:

• Greater \( \theta \) → more force downhill (\( mg \sin\theta \))
• Lower normal force (\( N = mg \cos\theta \))

Ultimately, the maximum angle before sliding begins can be calculated using static friction values. Once the component of gravitational pull that tries to overcome static friction matches the actual available friction, the bed's tilt boundary is reached. That point is when "\( \tan\theta = \mu_s \)" defines how steep the slope can be before sliding kicks in.