In our daily lives, objects are often acted upon by more than one force simultaneously, such as in a tug-of-war competition or a moving vehicle. When multiple forces act on an object, their combined effect can be represented by a single overall force known as the resultant force. Understanding resultant force allows us to determine whether an object stays stationary, moves with uniform velocity, or accelerates in a particular direction.
Compare the Pythagoras rectangle, triangle of forces, and parallelogram of forces methods to find resultant force magnitude and direction.
For two forces at right angles, complete a rectangle. The diagonal is the resultant force.
Draw forces tip-to-tail for the triangle method, or tail-to-tail for the parallelogram method.
Resultant force is the single force that represents the vector sum of two or more forces acting on an object.
When forces are in a straight line, add them algebraically by assigning a positive sign to one direction and a negative sign to the opposite direction.
Complete a rectangle and use Pythagoras' theorem: \(F = \sqrt{F_1^2 + F_2^2}\) and \(\tan\theta = \frac{F_y}{F_x}\).
Construct accurate scale diagrams using the triangle of forces (tip-to-tail) or the parallelogram of forces (tail-to-tail).
A free body diagram shows all the forces acting on that object only. Forces exerted by the object on its surroundings are not shown.
According to Newton's Second Law, \(F = ma\). If \(F = 0\), the object remains at rest or travels at constant velocity. If \(F \neq 0\), the object accelerates in the direction of the resultant force.
Answer in your mind, then press "Check Answer".
What is the resultant force acting on an object if a force of \(11\text{ N}\) acts to the left, while forces of \(9\text{ N}\) and \(17\text{ N}\) act to the right?
Two forces of \(240\text{ N}\) horizontally to the right and \(180\text{ N}\) vertically upwards act on a ball at the same time. Calculate the magnitude of the resultant force.
A passenger of mass \(50\text{ kg}\) stands in an elevator that accelerates upwards at \(2.0\text{ m s}^{-2}\). Taking \(g = 9.81\text{ m s}^{-2}\), what is the normal reaction \(R\) exerted by the floor on the passenger?
An object moving forward always has a net force acting forward in the direction of motion.
An object moving forward at a constant speed has a resultant force of zero (\(F = 0\text{ N}\)). A forward resultant force is only required to accelerate or change velocity.
The normal reaction of an object in a lift is always equal to its true gravitational weight (\(mg\)).
The normal reaction \(R\) equals \(mg\) only when the lift is stationary or moving with uniform velocity. When accelerating upwards, \(R = mg + ma\) (apparent weight is greater); when accelerating downwards, \(R = mg - ma\) (apparent weight is smaller).
Objective: Identify resultant force, free body diagrams, and Newton's Second Law.
1 Which of the following conditions is true for an object moving with a uniform velocity?
2 Two perpendicular forces of \(6\text{ N}\) and \(8\text{ N}\) act on an object. What is the magnitude of the resultant force?
3 The single force that represents the vector sum of two or more forces acting on an object is called the .
4 In a vector force table experiment, as the angle between two applied forces increases, the magnitude of their resultant force .
Match each state of motion of an object to its corresponding resultant force condition. If using a phone, tap the answer first, then tap the matching box.
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