what are newton's laws of motion
Answers
Explanation:
three fundamental laws of classical physics. The first states that a body continues in a state of rest or uniform motion in a straight line unless it is acted on by an external force. The second states that the rate of change of momentum of a moving body is proportional to the force acting to produce the change. The third states that if one body exerts a force on another, there is an equal and opposite force (or reaction) exerted by the second body on the first.
Newton’s First Law of Motion (Law of Inertia)
→ Any object remains in the state of rest or in uniform motion along a straight line, until it is compelled to change the state by applying external force.
Explanation: If any object is in the state of rest, then it will remain in rest until a external force is applied to change its state. Similarly, an object will remain in motion until any external force is applied over it to change its state. This means all objects resist to in changing their state. The state of any object can be changed by applying external forces only.
Second Law of Motion
→ Rate of change of momentum of an object is proportional to applied unbalanced force in the direction of force.
Mathematical expression
Suppose,
Mass of an object = m kg
Initial velocity of an object = u m/s
Final velocity of an object = v m/s
∴ Initial momentum, p1 = mu
Final momentum, p2 = mv
∴ Change in momentum = Final momentum – Initial momentum
= mv – mu
= m(v – u)
∴ Rate of change of momentum = Change in momentum/Time taken
= m(v-u)/t
• According to 2nd law, this rate of change is momentum is directly proportional to force.
We know that, a = (v-u)/t (From 1st equation of motion)
∴ F = kma
where, k is a constant. Its value can be assumed as 1.
∴ F = 1 × m × a = ma
• SI unit = kg m/s 2 or Newton
1 Newton: When an acceleration of 1 m/s2 is seen in a body of mass 1 kg, then the force applied on the body is said to be 1 Newton.
Proof of Newton’s First Law of Motion from Second Law
→ First law states that if external force F = 0, then a moving body keeps moving with the same velocity, or a body at rest continues to be at rest.
∴ F = 0
We know, F = m(v-u)/t
(i) A body is moving with initial velocity u then,
m(v-u)/t = 0 ⇒ v – u = 0
∴ v = u
Thus, final velocity is also same.
(ii) A body is at rest i.e., u = 0
Therefore, from above u = v = 0
So, the body will continue to be at rest.
Third Law of Motion
→ For every action there is an equal an opposite reaction.
Applications:-
(i) Walking is enabled by 3rd law.
(ii) A boat moves back when we deboard it.
(iii) A gun recoils.
(iv) Rowing of a boat.
Law of Conservation of Momentum
→ When two (or more) bodies act upon one another, their total momentum remains constant (or conserved) provided no external forces are acting.
• Initial momentum = Final momentum
Suppose, two objects A and B each of mass m1 and mass m2 are moving initially with velocities u1 and u2, strike each other after time t and start moving with velocities v1 and v2 respectively.
Now,
Initial momentum of object A = m1u1
Initial momentum of object B = m2u2
Final momentum of object A = m1v1
Final momentum of object B = m2v2
So, Rate of change of momentum in A,
F1 = (m1v1 - m1u1)t = m1(v1 - u1)/t ....(i)
Rate of change of momentum in B,
F2 = (m2v2 - m2u2)t = m2(v2 - u2)/t ....(ii)
We know from 3rd law of motion, F1 = −F2
So, m1(v1 - u1)/t = -m2(v2 - u2)/t
⇒ m1v1 – m2u2 = −m2v2 + m1u1
⇒ m1u1 + m2u2 = m1v1 + m2v2
Thus, Initial momentum = Final momentum