Forces are involved in most of our daily activities and can change the state of motion of an object. When a force acts on an object along a straight line, it changes the object's velocity, causing acceleration and altering its momentum over time.
Compare the two direct proportionality graphs and see how they combine to formulate Newton's Second Law.
When mass is constant, acceleration is directly proportional to force. The graph is a straight line passing through the origin.
When force is constant, acceleration is inversely proportional to mass. The graph is a straight line passing through the origin.
Combining the two relationships
Newton's Second Law of Motion: the rate of change of momentum is directly proportional to the force and acts in the direction of the applied force.
When an unbalanced force acts on an object, the object accelerates in the direction of the force. If the mass is kept constant, applying a larger force produces a proportionally larger acceleration (\(a \propto F\)).
If the applied force is kept constant, an object with a larger mass will experience a smaller acceleration. Acceleration is inversely proportional to mass (\(a \propto \frac{1}{m}\)).
The rate of change of momentum is directly proportional to the force and acts in the direction of the applied force. Mathematically, \(F \propto ma\) and \(F = ma\).
In S.I. units, 1 N is the force that produces an acceleration of \(1\ \mathrm{m\,s^{-2}}\) when applied on a mass of \(1\ \mathrm{kg}\).
Derivation of Newton's Second Law
Since \(a = \dfrac{v - u}{t}\), the rate of change of momentum is \(\dfrac{mv - mu}{t}\).
Answer in your mind, then press "Check Answer".
State Newton's Second Law of Motion.
Define the unit of force, 1 newton (1 N).
A force of 80 N acts on a stationary object for 7 s and causes it to reach a velocity of 35 m s⁻¹. Calculate the mass of the object.
A constant force is needed to keep an object moving at a constant velocity.
According to \(F = ma\), if velocity is constant, acceleration \(a = 0\), so the net force \(F = 0\). A net force causes an object to change velocity (accelerate), not simply maintain it.
Doubling the mass of an object will double its acceleration under the same force.
Acceleration is inversely proportional to mass (\(a \propto \frac{1}{m}\)). Doubling the mass halves the acceleration when the force is constant.
Objective: Test your understanding of force, mass, acceleration and Newton's Second Law.
1 What happens to the acceleration of a trolley if the pulling force applied on it is doubled while its mass is kept constant?
2 According to Newton's Second Law of Motion, the applied force acting on an object is directly proportional to the:
3 In S.I. units, 1 N is the force that produces an acceleration of 1 m s⁻² when applied on a mass of kg.
4 When a constant force acts on an object, its acceleration is inversely proportional to its .
Drag each term to the correct meaning. If using a phone, tap the answer first, then tap the matching box.
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