Balanced & Unbalanced forces

Balanced Forces:

• Equal & Opposite forces
• Do not cause any change in motion

Unbalanced Forces:

• Unequal forces
• Can be in the same or opposite direction
• Causes a change in motion

Momentum

Newton’s first law was for scenarios where net force = 0. The second law is for scenarios with net force not equal to 0. Momentum plays a crucial role in Second law.

• Momentum is the product of mass of a body & its velocity
• It is a Vector quantity
• It is denoted by p = mv

For example, A ball of 1 kg moving with 10m/sec has a momentum 10kg m/sec.

Momentum of a system remains conserved. Therefore,

• Greater force is required to set heavier bodies in motion

Newton’s Second Law

• The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.
• Alternatively, the relationship between an object’s mass m, its acceleration a, and the applied force F is F = ma; the direction of the force vector is the same as the direction of acceleration vector.

F ∝ dp/dt  [Greater the change in momentum, greater is force]

F = k dp/dt

F = dp/ dt

F = d/ dt (mv)

Let, m: mass of the body be constant

F = m dv/dt

F = ma

• Newton’s Second law is consistent with the First law

F = ma

If F =0, then a = 0

According to First law, if a = 0, Then F = 0

Thus, both the laws are in sync.

• Vector form of Newton’s Second law

Solution.

 m = 2 * 10³

 u = 36 km/hr = 10m/s

 s = 50m

 v = 0

To find: a, F, t

Third equation of motion: v² = u² + 2as

0 = 100 + 2a * 50

Or,  a = -1 m/s²

Therefore, F = ma = (2 * 10³ ) * 1 = 2 * 10³ N

V = u + at

0 = 10 – t

 t = 10 sec

Problem 2: The only force acting on a 5kg object has components F_x = 15N and F_y = 25N. Find the acceleration of the object.

 Solution.

   m= 5kg

Fx = 15N, Fy = 25N

F = Fxi + Fyj