Solved Examples of Kinetic Friction: Mastering AP Physics C

📚 Quick Study Guide

• 🧊[Definition] Kinetic friction is the force that opposes the motion of two surfaces sliding against each other.
• 📏[Formula] The magnitude of kinetic friction ($f_k$) is given by $f_k = \mu_k N$, where $\mu_k$ is the coefficient of kinetic friction and $N$ is the normal force.
• 🤔[Coefficient] The coefficient of kinetic friction ($\mu_k$) is a dimensionless quantity that depends on the nature of the two surfaces in contact. It is generally less than the coefficient of static friction.
• 📐[Direction] Kinetic friction always acts parallel to the surface and opposite to the direction of motion.
• 💡[Tip] Remember to always calculate the normal force correctly, as it directly affects the kinetic friction force. For example, on an inclined plane, $N = mg \cos(\theta)$.

🧪 Practice Quiz

1. A 5 kg block is sliding across a horizontal surface with an initial velocity of 10 m/s. The coefficient of kinetic friction between the block and the surface is 0.2. What is the magnitude of the kinetic friction force acting on the block?
   1. 9.8 N
   2. 4.9 N
   3. 10 N
   4. 19.6 N
2. A 2 kg block is pulled horizontally with a force of 15 N. The coefficient of kinetic friction between the block and the surface is 0.3. What is the acceleration of the block?
   1. 7.5 m/s²
   2. 6.03 m/s²
   3. 9.8 m/s²
   4. 4.5 m/s²
3. An object with mass $m$ is moving on a rough horizontal surface with coefficient of kinetic friction $\mu_k$. A force $F$ is applied at an angle $\theta$ above the horizontal. The magnitude of the frictional force is:
   1. $\mu_k mg$
   2. $\mu_k (mg - F \sin(\theta))$
   3. $\mu_k (mg + F \sin(\theta))$
   4. $\mu_k F \cos(\theta)$
4. A block slides down an inclined plane with a constant speed. The angle of inclination is 30 degrees. What is the coefficient of kinetic friction between the block and the plane?
   1. 0.577
   2. 0.866
   3. 0.5
   4. 1.732
5. A box of mass 10 kg is being pulled across a horizontal floor at a constant speed by a rope that makes an angle of 30 degrees with the floor. The tension in the rope is 50 N. What is the coefficient of kinetic friction between the box and the floor?
   1. 0.22
   2. 0.43
   3. 0.50
   4. 0.35
6. A car is traveling at a constant speed on a level road. The coefficient of kinetic friction between the tires and the road is 0.8. What is the minimum stopping distance if the initial speed of the car is 20 m/s? (Assume all four wheels brake equally).
   1. 25.5 m
   2. 31.9 m
   3. 19.1 m
   4. 15.3 m
7. Two blocks, A and B, with masses $m_A$ and $m_B$ respectively, are connected by a string that passes over a pulley. Block A is on a horizontal surface with a coefficient of kinetic friction $\mu_k$, and block B hangs vertically. If $m_A = 2m_B$, what is the acceleration of the system? (Assume $g$ is the acceleration due to gravity.)
   1. $g(1 - 2\mu_k)/3$
   2. $g(1 + 2\mu_k)/3$
   3. $g(1 - \mu_k)/3$
   4. $g(1 + \mu_k)/3$