Newton's Second Law of Motion

Derive the unit of force using the second law of motion. A force of $5 \mathrm{N}$ produces an acceleration of $8 {\mathrm{ms}}^{-2}$ on a mass $m_1$ and an acceleration of $24 {\mathrm{ms}}^{-2}$ on a mass $m_2$. What acceleration would the same force provide if both stones are tied together?

What is momentum? Write its SI unit. Interpret force in terms of momentum? Represent the following graphically.

(a) Momentum versus velocity when mass is fixed.

(b) Momentum versus mass when velocity is constant.

Using second law of motion, derive the relation between force and acceleration. A bullet of $10 \mathrm{g}$ strikes a sand-bag at a speed of ${10}^3 {\mathrm{ms}}^{-1}$ and gets embedded after travelling $5 \mathrm{cm}$. Calculate 
(i) the resistance force exerted by the sand on the bullet. 
(ii) the time taken by the bullet to come to rest.

A car initially at rest, picks up a velocity of $72 \mathrm{km}/\mathrm{h}$ in $20$ seconds. If the mass of the car is $1000 \mathrm{kg}$, calculate: (i) the force developed by its engine, and (ii) the distance covered by the car in $20$ seconds.

A force of  $500 \mathrm{N}$ acts on a body of mass $x$ and gives it an acceleration of $200 \mathrm{m} {\mathrm{s}}^{-2}$. The same force acting on another body of mass $y$  gives it an acceleration of $40 \mathrm{m} {\mathrm{s}}^{-2}$. If $x$ and  $y$ are tied together and the same force as above, acts on them, what acceleration is produced in the combination?

A force of $100 \mathrm{N}$ gives a body of mass $m_1$, an acceleration of $5 \mathrm{m}/{\mathrm{s}}^2$. The same force can give an acceleration of $40 \mathrm{m}/{\mathrm{s}}^2$ to another body of mass $m_2$. If both the bodies are tied together and acted upon by the same force as above, what acceleration is produced in the combination?

Two blocks of different metals, but identical in shape and size, are acted upon by equal forces, such that the acceleration of the second block is $3$ times more than that of the first block. What is the ratio of the mass of the second block with respect to that of the first block?

A cyclist and a person on a moped are acted upon by the same force. If the acceleration produced by the cyclist is only $\frac{2}{5}$th that of the moped, calculate the ratio of the masses of the cyclist and the moped.

The engine of a truck of mass $4$ ton, produces a force of $7500 \mathrm{N}$. Calculate the acceleration of the truck produced by the engine.

Calculate the mass of a body, when a force of $525 \mathrm{N}$, produces an acceleration of $3.5 \mathrm{m}/{\mathrm{s}}^2$?

What force will produce an acceleration of $3.5 \mathrm{m}/{\mathrm{s}}^2$, in a body of mass $12.5 \mathrm{kg}$?                
 

A truck of mass $M$ is moved under a force $F$. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved, then how does the acceleration change ?

Velocity versus time graph of a ball of mass $50 \mathrm{g}$ rolling on a concrete floor is shown in figure. Calculate the acceleration and frictional force of the floor on the ball.

Prove mathematically: $\mathrm{F}=\mathrm{ma}$, where $\mathrm{F}$is the force impressed on a body, $\text{'}\mathrm{m}\text{'}$ the mass and $\text{'}a\text{'}$ the acceleration.

Define Newton’s second law of motion:

 A force $F$ produces an acceleration $a$ in a body. The same force produces an acceleration $4a$ in another body. The mass of the other body is:

Force remaining constant, if the mass of body increases, its acceleration is likely to:

A force of magnitude $F$ acts on a body of mass $m$. The acceleration of the body depends upon :

A force of magnitude $F$ acts on a body of mass $m$. The acceleration of the body depends upon :