Balanced & Unbalanced forces
- Equal & Opposite forces
- Do not cause any change in motion
- Unequal forces
- Can be in the same or opposite direction
- Causes a change in motion
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
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 Fx = 15N and Fy = 25N. Find the acceleration of the object.
Fx = 15N, Fy = 25N
F = Fxi + Fyj