Define force. Derive the formula for force.
A push or a pull on an object is known as Force.
Suppose an object of mass, m is moving along a straight line with an initial velocity, u. It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time, t. The initial and final momentum of the object will be, p1=mu and p2=mv respectively.
The change in momentum ∝ p2–p1
∝ mv–mu
∝ m×(v−u)
The rate of change of momentum ∝m(v−u)t
Or, the applied force,
F ∝m(v−u)t
F=km(v−u)t
F=kma
Here [a=(v−u)t] is the acceleration, which is the rate of change of velocity. The quantity, k is a constant of proportionality. The SI units of mass and acceleration are kg and ms−2 respectively. The unit of force is so choosen that the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produced an acceleration of 1 ms−2 in an object of 1 kg mass. That is, 1 unit of force=k×(1kg)×(1 ms−2).
Thus, the value of k becomes 1.Hence
F=ma
The unit of force is kgms−2 or newton, which has the symbol N. The second law of motion gives us a method to measure the force acting on an object as a product of its mass and acceleration.
A push or a pull on an object is known as Force.
Suppose an object of mass, m is moving along a straight line with an initial velocity, u. It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time, t. The initial and final momentum of the object will be, p1=mu and p2=mv respectively.
The change in momentum ∝ p2–p1
∝ mv–mu
∝ m×(v−u)
The rate of change of momentum ∝m(v−u)t
Or, the applied force,
F ∝m(v−u)t
F=km(v−u)t
F=kma
Here [a=(v−u)t] is the acceleration, which is the rate of change of velocity. The quantity, k is a constant of proportionality. The SI units of mass and acceleration are kg and ms−2 respectively. The unit of force is so choosen that the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produced an acceleration of 1 ms−2 in an object of 1 kg mass. That is, 1 unit of force=k×(1kg)×(1 ms−2).
Thus, the value of k becomes 1.Hence
F=ma
The unit of force is kgms−2 or newton, which has the symbol N. The second law of motion gives us a method to measure the force acting on an object as a product of its mass and acceleration.
