In Fig. 6-21, a block of mass m 5.0 kg is at rest on a...

In Fig. 6-21, a block of mass
m 5.0 kg is at rest on a ramp.The coefficient of static friction between the
block and ramp is not known. Find the
magnitude of the net force exerted
by the ramp on the block.

Key Concepts

Net Contact Force

The net force exerted by a surface on an object is the vector sum of the normal and frictional forces, collectively known as the contact force. In equilibrium problems such as this, even though the object remains at rest, the contact force can be determined by considering how it balances the external forces (for instance, gravity) acting on the object.

Frictional Force

Friction, particularly static friction in equilibrium situations, acts parallel to the surface and opposes the potential motion of the object. In equilibrium on an incline, static friction adjusts in magnitude (up to its maximum limit) to exactly counteract the component of the gravitational force that is parallel to the surface.

Force Decomposition on Inclined Planes

When analyzing forces on an incline, it is essential to resolve the gravitational force into two perpendicular components: one parallel to the plane, which tends to slide the object down, and one perpendicular to the plane, which is balanced by the normal force. This decomposition simplifies the analysis of how different forces interact on an incline.

Static Equilibrium

This principle states that when an object is at rest, the sum of all forces acting on it must be zero. In problems like this, the forces acting on the object—including gravitational, frictional, and normal forces—balance each other so that there is no net acceleration.

Normal Force

The normal force is the contact force exerted by a surface perpendicular to itself. On an inclined plane, the normal force balances the perpendicular component of the gravitational force and is a key part of the net contact force exerted by the surface on the object.

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