AP Physics C: Mechanics Questions on Net Force with Solutions

📚 Quick Study Guide

🔍 Newton's First Law: An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a net force. 💡 Newton's Second Law: The net force acting on an object is equal to the mass of the object times its acceleration: $F_{net} = ma$. 📝 Newton's Third Law: For every action, there is an equal and opposite reaction. ⚖️ Net Force: The vector sum of all forces acting on an object. To find the net force, resolve forces into components (usually x and y), sum the components in each direction, and then use the Pythagorean theorem to find the magnitude of the net force and trigonometry to find its direction. 📐 Free-Body Diagrams: Essential for visualizing and analyzing forces acting on an object. Always draw a clear diagram showing all forces. ➕ Superposition: Forces add as vectors. If you have multiple forces, you must add them vectorially to find the net force. 🧱 Common Forces: Gravity ($F_g = mg$), Tension ($T$), Normal Force ($N$), Friction ($F_f = \mu N$), Spring Force ($F_s = -kx$).

🧪 Practice Quiz

1. A block of mass $m$ is pulled across a horizontal surface with a force $F$ at an angle $\theta$ above the horizontal. The coefficient of kinetic friction between the block and the surface is $\mu$. What is the magnitude of the normal force on the block?
   1. $mg$
   2. $mg - F\cos\theta$
   3. $mg + F\sin\theta$
   4. $mg - F\sin\theta$
2. A 2 kg block is pushed up an inclined plane with a force of 15 N. The plane is inclined at an angle of 30 degrees to the horizontal. If the coefficient of kinetic friction between the block and the plane is 0.2, what is the acceleration of the block?
   1. $0.5 m/s^2$
   2. $1.0 m/s^2$
   3. $1.5 m/s^2$
   4. $2.0 m/s^2$
3. A 5 kg object is suspended from a ceiling by two ropes that make angles of 30 degrees and 60 degrees with the horizontal. What is the tension in the rope that makes an angle of 30 degrees with the horizontal?
   1. $24.5 N$
   2. $49 N$
   3. $21.2 N$
   4. $28.3 N$
4. A car of mass 1000 kg is moving at a constant velocity of 20 m/s on a level road. The coefficient of rolling friction between the tires and the road is 0.02. What is the magnitude of the force required to maintain this constant velocity?
   1. $100 N$
   2. $200 N$
   3. $300 N$
   4. $400 N$
5. A block of mass $m$ is placed on a frictionless inclined plane that makes an angle $\theta$ with the horizontal. What is the magnitude of the normal force exerted on the block by the inclined plane?
   1. $mg$
   2. $mg \sin\theta$
   3. $mg \cos\theta$
   4. $mg \tan\theta$
6. Two blocks are connected by a string that passes over a frictionless pulley. The mass of block 1 is 3 kg, and the mass of block 2 is 5 kg. If the blocks are released from rest, what is the magnitude of the acceleration of the blocks?
   1. $2.45 m/s^2$
   2. $4.9 m/s^2$
   3. $9.8 m/s^2$
   4. $19.6 m/s^2$
7. A box with a weight of 50 N rests on a horizontal surface. A horizontal force of 20 N is required to start the box moving. Once the box is moving, a force of 10 N is sufficient to keep it moving at a constant speed. What is the coefficient of static friction between the box and the surface?
   1. 0.1
   2. 0.2
   3. 0.4
   4. 0.5