1. **Problem Statement:** We need to understand the differences between friction on a horizontal plane and friction on an inclined plane. 2. **Friction Basics:** Friction is a force that opposes the relative motion or tendency of such motion of two surfaces in contact. 3. **Friction on a Horizontal Plane:** - The frictional force $f$ is given by $f = \mu N$, where $\mu$ is the coefficient of friction and $N$ is the normal force. - On a horizontal plane, the normal force $N$ equals the weight of the object, $N = mg$, where $m$ is mass and $g$ is acceleration due to gravity. - Therefore, frictional force is $f = \mu mg$. 4. **Friction on an Inclined Plane:** - The normal force $N$ is less than the weight because it is the component perpendicular to the inclined surface: $N = mg \cos \theta$, where $\theta$ is the angle of inclination. - The frictional force is $f = \mu N = \mu mg \cos \theta$. - The component of weight parallel to the incline is $mg \sin \theta$, which tends to move the object down. 5. **Key Differences:** - On a horizontal plane, friction depends on the full weight $mg$. - On an inclined plane, friction depends on $mg \cos \theta$, which decreases as $\theta$ increases. - This means frictional force is generally less on an inclined plane compared to a horizontal plane for the same object. 6. **Summary:** - Frictional force formula is the same but the normal force differs. - Normal force on horizontal plane: $N = mg$. - Normal force on inclined plane: $N = mg \cos \theta$. - Frictional force decreases with increasing incline angle due to reduced normal force.