Advertisements
Advertisements
प्रश्न
Prove mathematically F = ma
उत्तर
Derivation of F = ma from Newton’s Second Law of Motion:
Newton introduced the concept of momentum and say “The momentum of a moving body is defined as the product of its mass and velocity.”
Thus, p = mv, where p = momentum of body
m = mass of body
v = velocity of body
Suppose the velocity of body of mass m changes from u to v in time t.
Initial momentum, p1 = mu
and final momentum, p2 = mv
the change in momentum, (p2 − p1) takes place in time t. Then according to Newton’s second law of motion, the magnitude of force F is:
`("P"_2-"P"_1)/"t"` α F, or F = `("km"("v"-"u"))/"t"`
Where k = constant of proportionality
Now, `"a"(("v"-"u"))/"t"`, where a = acceleration of body
∴ F = k ma
⇒ F = ma .............(∵ k = 1, constant)
This relation holds good when mass of the body remains constant.
APPEARS IN
संबंधित प्रश्न
A helicopter of mass 1000 kg rises with a vertical acceleration of 15 m s–2. The crew and the passengers weigh 300 kg. Give the magnitude and direction of the
(a) force on the floor by the crew and passengers,
(b) action of the rotor of the helicopter on the surrounding air,
(c) force on the helicopter due to the surrounding air.
A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the other end in the following figure. Show that whatever force the monkey exerts on the rope, the monkey and the block move in the same direction with equal acceleration. If initially both were at rest, their separation will not change as time passes.
Two bodies A and B of same mass are moving with velocities v and 2v, respectively. Compare their (i) inertia and (ii) momentum.
Calculate the velocity of a body of mass 0.5 kg, when it has a linear momentum of 5 Ns.
Define Newton’s second law of motion.
What causes motion in a body?
Which of the following has the largest inertia?
Use Newton's second law to explain the following:
We always prefer to land on sand instead of hard floor while taking a high jump.
A body of mass 2 kg travels according to the law x(t) = pt + qt2 + rt3 where p = 3 ms−1, q = 4 ms−2 and r = 5 ms−3. The force acting on the body at t = 2 seconds is ______.
The position time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 0 s and t = 4 s.
