## Motion of Bodies in Contact | Definition, Types – Laws of Motion

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

**Motion of Bodies in Contact**

1. **Contact Force Between Two Blocks:**

If force F is applied on an object of mass m_{1}, then acceleration of the bodies

Contact force on m_{1} = m_{1}a = \(\frac{m_{1} F}{\left(m_{1}+m_{2}\right)}\)

Contact force on m_{2} = m_{2}a = \(\frac{m_{2} F}{\left(m_{1}+m_{2}\right)}\)

2. **Contact Force Between Three Blocks:**

If force F is applied on an object of mass m_{1}, then acceleration of the bodies

= \(\frac{F}{\left(m_{1}+m_{2}+m_{3}\right)}\)

Contact force between m_{1} and m_{2}

\(F_{1}=\frac{\left(m_{2}+m_{3}\right) F}{\left(m_{1}+m_{2}+m_{3}\right)}\)

Contact force between m_{2} and m_{3}

\(F_{2}=\frac{m_{3} F}{\left(m_{1}+m_{2}+m_{3}\right)}\)

3. **Motion of Two Bodies One Resting on the Other:**

(a) The coefficient of friction between surface of A and B be μ. If a force F is applied on the lower body A, then common acceleration of two bodies

Pseudo force acting on block B due to the accelerated motion,

f’ = ma

The pseudo force tends to produce a relative motion between bodies A and B and consequently a frictional force

f = μ N = μmg is developed.

For equilibrium, ma ≤ μmg or a ≤ μg

(b) Let friction is also present between the ground surface and body A Let the coefficient of friction between the given surface and body A is μ_{1} and the coefficient of friction between the surfaces of bodies A and B is μ_{2}. If a force F is applied on the lower body A.

Net accelerating force F – f_{A} = F – μ_{1} (M + m)g

∴ Net acceleration

\(a=\frac{F-\mu_{1}(M+m) g}{(M+m)}=\frac{F}{(M+m)}-\mu_{1} g\)

Pseudo force acting on the block B,

f’ = ma

The pseudo force tends to produce a relative motion between the bodies A and B are consequently a frictional force f_{B} = μ_{2} mg is developed. For equilibrium

ma ≤ μ_{2}mg or a ≤ μ_{2}g

If acceleration produced under the the effect of force Fis more than μ_{2}g, then two bodies will not move together.

4. **Motion of Bodies Connected by a String:**

Acceleration of the system a = \(\frac{F}{\left(m_{1}+m_{2}+m_{3}\right)}\)

Tension in string

T_{1} = F

T_{2} = (m_{2} + m_{3}) a = \(\frac{\left(m_{2}+m_{3}\right) F}{\left(m_{1}+m_{2}+m_{3}\right)}\)

T_{3} = m_{3}a = \(\frac{m_{3} F}{\left(m_{1}+m_{2}+m_{3}\right)}\)

**Laws of Motion:
**There are various laws in Physics that define the motion of the object. When an object is in motion whether it is linear or circular there is some force which is always imposed on it.