An object is in equilibrium of forces when the forces acting on it produce a zero resultant force. Learn how to sketch triangles of forces and solve equilibrium problems using resolution of forces and scaled drawings.
See how three coplanar forces in equilibrium form a closed vector triangle and how forces are resolved parallel and perpendicular to an inclined plane.
Three non-parallel forces in equilibrium can be drawn tip-to-tail to form a closed triangle. The lengths of the sides represent the magnitudes of the forces.
Weight \(W\) is resolved into components parallel and perpendicular to the plane. Normal reaction \(R = W\cos\theta\) and friction \(F_R = W\sin\theta\).
An object is in equilibrium of forces when the forces acting on it produce a zero resultant force. According to Newton's Second Law, \(F = ma\), when \(a = 0\), the resultant force is zero.
An object in equilibrium can be stationary or moving with uniform velocity. In both cases, acceleration is zero, so the resultant force is zero.
For three non-parallel forces in equilibrium, the force vectors drawn in sequence tip-to-tail form a closed triangle of forces.
Resolution of forces splits an inclined force into horizontal and vertical components. For equilibrium, \(\sum F_x = 0\) and \(\sum F_y = 0\).
For a plane inclined at angle \(\theta\) to the horizontal, the component of weight perpendicular to the plane is \(W\cos\theta\) and the component parallel to the plane is \(W\sin\theta\). Therefore, normal reaction \(R = W\cos\theta\) and frictional force \(F_R = W\sin\theta\).
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What is meant by forces in equilibrium?
If an object is acted on by three forces in equilibrium, what shape do the force vectors form when drawn in sequence head-to-tail?
A box of weight \(50\text{ N}\) is stationary on an inclined plane of \(40^\circ\). What is the magnitude of the frictional force acting on the box?
If an object is moving, forces cannot be in equilibrium.
If an object is moving at constant velocity in a straight line, its acceleration is zero. By \(F = ma\), the resultant force is zero, so the forces are in equilibrium.
The normal reaction \(R\) on an inclined plane is always equal to the weight \(W\).
The normal reaction is perpendicular to the inclined surface, so it balances only the perpendicular component of weight, \(R = W\cos\theta\), which is less than \(W\).
Objective: Check your understanding of forces in equilibrium, triangle of forces and resolution of forces.
1 An object is said to be in equilibrium of forces when:
2 When three forces of equal magnitude act on an object such that the object is in equilibrium, what is the angle between each adjacent force?
3 For a stationary box of weight \(W\) resting on a plane inclined at angle \(\theta\) to the horizontal, the normal reaction \(R\) is balanced by the component of weight equal to .
4 When three forces acting on an object are in equilibrium, the vectors drawn in sequence tip-to-tail will form a closed .
Match each physical force on an inclined plane or hanging system to its correct description or expression. If using a phone, tap the answer first, then tap the matching box.
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