Resultant force & Newton's laws
Kinematics described motion. Forces explain why velocity changes. A force is a push or pull on a body; the resultant forceis the vector total of all the forces acting on that body.
A non-zero resultant force gives acceleration
Definition
What is meant by Newton's first law?
Model answer: A body remains at rest or continues to move with constant velocity unless acted on by a non-zero resultant force.
Swipe left or right to see the whole diagram →
- Zero resultant force means zero acceleration. The body may be at rest or moving at constant velocity.
- A non-zero resultant force gives acceleration in the direction of that resultant.
- The same resultant produces a smaller acceleration when the mass is larger.
Acceleration is the rate at which velocity changes. It can change the speed, the direction of motion, or both.
Common mistake
Turn the force diagram into one signed equation
Definition
What is meant by Newton's second law?
Model answer: The resultant force on a body is equal to the product of its mass and acceleration.
Symbols
- = add the signed forces in the chosen direction; Σ means add (N)
- = mass (kg)
- = signed acceleration in the chosen direction (m s⁻²)
Swipe left or right to see the whole diagram →
One newton is the force that gives a 1 kg mass an acceleration of 1 m s⁻²: .
- Isolate the body: focus on that body and draw only forces acting on it.
- Choose and mark one positive direction.
- Give every force a sign from that direction.
- Write signed forces on the left and on the right.
- Solve, then translate the sign of the answer.
Worked example
Driving force and resistance
A 1200 kg car has a driving force of 900 N and a resistance of 300 N. Take the direction of motion as positive.
Key idea
Include a resistance force only when the question states or indicates one.
Use Newton first, then continue with kinematics
Newton's law finds the acceleration. If the forces and mass are constant, that acceleration is constant, so a constant-acceleration equation can then answer the motion part.
Worked example
From forces to a future velocity
The car above travels initially at 5 m s⁻¹. Find the time required to reach 17 m s⁻¹ while the forces remain unchanged.
Common mistake
An 800 kg car travels at 8 m s⁻¹. Its engine produces a constant driving force of 1400 N and the total resistance is 440 N. Find its acceleration, speed after 10 s and distance travelled in those 10 s.