### Forces On Bodiesproblems Involving Multiple Bodies

**Concepts to Remember**

**1. Multiple Forces Acting on a Body:**

- Imagine pushing a box with one hand while someone else is pulling it in the opposite direction. These opposing forces affect the box’s motion.

**2. Newton’s Laws of Motion:**

- Newton’s first law: An object at rest stays at rest, while an object in motion stays in motion with an unchanged velocity unless acted upon by an external force.
- Newton’s second law: The acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
- Newton’s third law: Every action has an equal and opposite reaction.

**3. Drawing and Resolving Vectors:**

- Represent forces as vectors (arrows) with magnitude (length) and direction. Decompose forces into their components (e.g., horizontal and vertical).

**4. Static Equilibrium:**

- When the net force on an object is zero, the object is in static equilibrium and won’t move unless external forces change.

**5. Pseudo Force:**

- In accelerating reference frames (like a moving car), non-inertial forces called “pseudo forces” seem to act on objects (e.g., feeling “thrown back” when accelerating).

**6. Concurrent and Non-Concurrent Forces:**

- Concurrent forces meet at a common point, while non-concurrent forces don’t. Calculate their resultant (combined effect) differently.

**7. Friction and Its Effects:**

- Friction opposes motion between two surfaces in contact. It affects objects by slowing them down or causing them to heat up.

**8. Terminal Velocity:**

- The constant velocity reached by an object falling through a fluid (like air or water) when the force of air resistance equals its weight.

**9. Projectile Motion:**

- The path followed by an object (e.g., a thrown ball) launched into the air. It combines horizontal and vertical motion affected by gravity.

**10. Centripetal Force:**

- The force that keeps objects moving in a circular path. Directed towards the center of rotation (e.g., the force keeping cars on a curved track).

**11. Work and Energy:**

- Work is the energy transferred when a force acts on an object over a displacement. Energy comes in different forms (e.g., kinetic and potential energy).

**12. Power:**

- Power is the rate at which work is done or energy is transferred (measured in watts).

**13. Impulse and Momentum:**

- Impulse (force x time) changes an object’s momentum (mass x velocity). According to Newton’s third law, impulses come in equal but opposite pairs.

**14. Conservation of Energy:**

- The total energy of a closed system remains constant, although it can change form (e.g., potential energy to kinetic energy).

**15. Conservation of Momentum:**

- The total momentum of a closed system remains constant, even when individual objects’ momenta change during interactions.