Derive the relationship F = ma, where each symbol has its usual significance. [5 MARKS]
Derive the relationship F = ma, where each symbol has its usual significance. [5 MARKS]
Explanation 5 Marks
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)
The rate of change of momentum ∝m(v−u)t
Or, the applied force, F∝m(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 chosen 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 1ms−2 in an object of 1kg mass. That is, 1N=1kg×1ms−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 it's mass and acceleration.
Explanation 5 Marks
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)
The rate of change of momentum ∝m(v−u)t
Or, the applied force, F∝m(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 chosen 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 1ms−2 in an object of 1kg mass. That is, 1N=1kg×1ms−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 it's mass and acceleration.
