State and apply each of Newton’s laws of motion to solve problems and answer exam questions.
Statement: An object at rest stays at rest, and an object in motion continues in a straight line at constant speed unless acted upon by an external force.
Analogy: Think of a soccer ball on a field – it won’t move until someone kicks it. Once kicked, it keeps rolling until friction or a goal post stops it.
Example: A 2 kg crate on a frictionless table remains stationary until a worker pushes it. The worker’s push is the external force that changes its state.
Exam tip: Look for phrases like “no net external force” or “constant velocity” to identify situations governed by the first law.
Statement: The net external force acting on an object is equal to the mass of the object multiplied by its acceleration: \$F_{\text{net}} = ma\$
Analogy: Pushing a shopping cart: the harder you push (larger force), the faster it accelerates. If the cart is heavier, you need a larger force to achieve the same acceleration.
Example: A 5 kg sled is pulled with a 20 N horizontal force. Its acceleration is \$a = \frac{F}{m} = \frac{20}{5} = 4\ \text{m/s}^2.\$
Exam tip: Always check the direction of the force and acceleration. Use a sign convention (positive to the right, negative to the left) to avoid mistakes.
Statement: For every action force, there is an equal and opposite reaction force.
Analogy: When you jump off a small boat, you push the boat backward while the boat pushes you forward with an equal force.
Example: A rocket expels exhaust gases at 3000 m/s. The rocket experiences an upward thrust equal in magnitude to the downward force on the gases.
Exam tip: Remember that the action–reaction pair acts on different objects. Don’t add them together when solving for a single object’s motion.
Definition: Momentum is the product of an object’s mass and velocity: \$p = mv\$
Conservation: In an isolated system with no external forces, total momentum remains constant.
Example: Two ice skaters (each 60 kg) push off each other. If one moves at 2 m/s to the right, the other moves at 1.33 m/s to the left to conserve momentum.
| Object | Mass (kg) | Velocity (m/s) | Momentum (kg·m/s) |
|---|---|---|---|
| Skater A | 60 | 2 | 120 |
| Skater B | 60 | -1.33 | -80 |
| Total | 40 |
Exam tip: When a problem involves multiple objects, set up equations for each using the third law to relate forces. Then solve simultaneously for unknowns.