According to this law, “the force acting on a body is directly proportional to the rate of change of linear momentum of the body and the change in momentum takes place in the direction of the force”.

**NEWTON’S SECOND LAW OF
MOTION**

According to this law,
“the force acting on a body is directly proportional to the rate of change of
linear momentum of the body and the change in momentum takes place in the
direction of the force”.

This law helps us to
measure the amount of force. So, it is also called as ‘*law of force*’.
Let, ‘m’ be the mass of a moving body, moving along a straight line with an
initial speed ‘u’ After a time interval of ‘t’, the velocity of the body
changes to ‘v’ due to the impact of an unbalanced external force F.

Initial momentum of the
body P_{i} = mu

Final momentum of the
body P_{f} = mv

Change in momentum Δp =
P_{f} –P_{i}

= mv – mu

By Newton’s second law
of motion,

Force, F ∝
rate of change of momentum

F ∝
change in momentum / time

Here, k is the
proportionality constant. k = 1 in all systems of units. Hence,

Since, acceleration =
change in velocity/ time, a=(v-u)/t. Hence, we have

**F = m × a (1.6)**

Force = mass × acceleration

No
external force is required to maintain the motion of a body moving with uniform
velocity. When the net force acting on a body is not equal to zero, then
definitely the velocity of the body will change. Thus, change in momentum takes
place in the direction of the force. The change may take place either in
magnitude or in direction or in both.

Force is required to produce the acceleration of a
body. In a uniform circular motion, even though the speed (magnitude of
velocity) remains constant, the direction of the velocity changes at every
point on the circular path. So, the acceleration is produced along the radius
called as *centripetal acceleration*.
The force, which produces this acceleration is called as centripetal force,
about which you have learnt in class IX.

**Units of
force: **SI unit of force is newton (N)** **and
in C.G.S system its unit is dyne.

**Definition of 1 newton (N): **The amount
of force required for a body of mass 1 kg produces an acceleration of 1 m *s*^{–2}, **1 N = 1 kg m** *s*^{–2}

**Definition of 1
dyne: **The amount of force required for a body of mass 1 gram produces an
acceleration of 1 cm *s*^{–2}, **1 dyne = 1 g cm** ** s^{–2};** also

**Unit force:**

The amount of force required
to produce an acceleration of 1 m *s*^{–2} in a body of mass kg is
called ‘*unit force*’.

**Gravitational unit of
force:**

In the SI system of
units, gravitational unit of force is kilogram force, represented by kg f. In
the CGS system its unit is gram force, represented by g f.

**1 kg f = 1 kg × 9.8 m s^{-2}
= 9.8 N;**

**1 g f = 1 g × 980 cm s^{-2}
= 980 dyne**

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10th Science : Chapter 1 : Laws of Motion : Newton’s Second Law of Motion |

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