Question
State Newton's third law of motion. Discuss its consequences.
✓
Answer
Newton's third law of motion states that for any action, there is equal and opposite reaction.
So, if a body applies a force F12 on body 2 (action), then body 2 also applies a force F21 on body 1 but in opposite direction, then
F21 = - F12
In terms of magnitude
|F21 | = | F12 |
It is very important to note that F12 and F21, though are equal in magnitude and opposite in direction yet act on different points or else no motion will be possible.
For example, hands pull up a chest expander (spring) and spring in turn exerts force on the arms. A football pressed reacts on the foot with the same force and so on.
The most important consequence of the third law of motion is the law of motion is the law of conservation of linear momentum and its application in collision problems.
Since $\text{F}_{12}=\text{F}_{21}$ and $\text{F}=\text{m}\frac{\Delta\upsilon}{\Delta\text{t}}$
$\therefore\text{m}_1\frac{\Delta\upsilon_1}{\Delta\text{t}}=-\text{m}_2\frac{\Delta\upsilon_2}{\Delta\text{t}}$
Here $\Delta\text{t}$ is the time for which the bodies come in contact during impact. This is same for the two bodies of masses m1 and m2 and having velocity changes $\Delta\text{v}_1$ and $\Delta\text{v}_2$ respectively.
Let $\text{u}_1,\text{u}_2$ and $\text{v}_1,\text{v}_2$ be the initial and final velocities of the two masses before and after collision, then,
$\text{m}_1(\text{v}_1-\text{u}_1)=\text{m}_2(\text{v}_2-\text{u}_2)$
or $\text{m}_1\text{u}_1+\text{m}_2\text{u}_2=\text{m}_1\text{v}_1+\text{m}_2\text{v}_2$
Momentum before impact = Momentum after impact.
(This is known as the law of conservation of momentum).
So, if a body applies a force F12 on body 2 (action), then body 2 also applies a force F21 on body 1 but in opposite direction, then
F21 = - F12
In terms of magnitude
|F21 | = | F12 |
It is very important to note that F12 and F21, though are equal in magnitude and opposite in direction yet act on different points or else no motion will be possible.
For example, hands pull up a chest expander (spring) and spring in turn exerts force on the arms. A football pressed reacts on the foot with the same force and so on.
The most important consequence of the third law of motion is the law of motion is the law of conservation of linear momentum and its application in collision problems.
Since $\text{F}_{12}=\text{F}_{21}$ and $\text{F}=\text{m}\frac{\Delta\upsilon}{\Delta\text{t}}$
$\therefore\text{m}_1\frac{\Delta\upsilon_1}{\Delta\text{t}}=-\text{m}_2\frac{\Delta\upsilon_2}{\Delta\text{t}}$
Here $\Delta\text{t}$ is the time for which the bodies come in contact during impact. This is same for the two bodies of masses m1 and m2 and having velocity changes $\Delta\text{v}_1$ and $\Delta\text{v}_2$ respectively.
Let $\text{u}_1,\text{u}_2$ and $\text{v}_1,\text{v}_2$ be the initial and final velocities of the two masses before and after collision, then,
$\text{m}_1(\text{v}_1-\text{u}_1)=\text{m}_2(\text{v}_2-\text{u}_2)$
or $\text{m}_1\text{u}_1+\text{m}_2\text{u}_2=\text{m}_1\text{v}_1+\text{m}_2\text{v}_2$
Momentum before impact = Momentum after impact.
(This is known as the law of conservation of momentum).
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