A body of mass $5 \mathrm{k}\mathrm{g}$ is acted upon by two perpendicular forces $8 \mathrm{N}$ and $6 \mathrm{N}$. Give the magnitude and direction of the acceleration of the body.

According to Newton’s first law of motion, everybody continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise.

2. Newton’s Second Law of Motion:

According to Newton’s second law of motion, 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. $F= \frac{dP}{dt}= ma$

3. Newton’s Third Law of Motion:

According to Newton’s third law of motion, to every action, there is always an equal and opposite reaction. ${\overrightarrow{F}}_{AB}= -{\overrightarrow{F}}_{BA}$ where ${\overrightarrow{F}}_{AB}=$Force on A due to B and ${\overrightarrow{F}}_{BA}=$ Force on B due to A

4. Law of Conservation of Linear Momentum:

According to law of conservation of linear momentum, the total momentum of an isolated system of interacting particles is conserved.

5. Weighing Machine:

A weighing machine does not measure the weight but measures the force exerted by object on its upper surface.

6. Spring Force:

Spring force $F= -kx$. Here, x is displacement of the free end from its natural length or deformation of the spring and k is spring constant.

7. Sprint Balance:

Spring balance does not measure the weight. It measures the force exerted by the object at the hook.

8. Atwood Machine:

For Atwood machine $a= \frac{\left(m_2-m_1\right)g}{m_1+m_2}, T= \frac{2m_1{m}_{2}g}{m_1+m_2}$

9. Kinetic and Static Friction:

(i) Kinetic friction magnitude due to contact surfaces on the bodies, $f_k= {\mu }_{k}N$. Here, constant μk is called the coefficient of kinetic friction and its value depends on the nature of the two surfaces in contact. 

(ii) Static friction exists between the two surfaces when there is tendency of relative motion but no relative motion along the two contact surfaces.

(iii) Static friction is a variable and self-adjusting force. The maximum value of static friction is called limiting friction and its value. $f_{s\max }= {\mu }_{s}N$, $\begin{array}{c}0<f_s<f_{s\max }\end{array}$

(iv) Kinetic friction is less than limiting friction. 

10. Maximum Velocity on a Curved road:

(i) On a flat road for a give radius of curvature of the turn $\left(R\right)$ and coefficient of friction value $\left({\mu }_s\right)$, maximum velocity $\left(V_{\max }\right)$with which a vehicle can take turn, $V_{\mathrm{m}\mathrm{a}\mathrm{x}}= \sqrt{{\mu }_{s}Rg}$

(ii) On a banked road with banking angle θ, radius of curvature of the turn $\left(R\right)$ and coefficient of friction value $\left({\mu }_s\right)$, maximum velocity ($V_{\mathrm{m}\mathrm{a}\mathrm{x}}$) with which a vehicle can take turn, $V_{\max }= {\left(Rg\frac{{\mu }_s+\tan \theta }{1-{\mu }_s\tan \theta }\right)}^{\frac{1}{2}}$