Forces
Key Concepts
- A force is a push or pull measured in Newtons (N) which is a substitute for kgm/s².
- An object cannot apply a force on itself.
- Forces are not needed to keep an object in motion, only to change motion.
- Any change in motion is caused by acceleration.
- F = ma → forces cause acceleration.
- Where F = force, m = mass, and a = acceleration.
Types of Forces
- ==Contact forces==: forces applied via physical contact between objects.
- ^^Applied force^^: the force a person exerts on an object.
- ^^Friction^^: the resisting force between two objects.
- Static: resists putting an object at rest into motion
- Kinetic: resists keeping an object in motion
- ^^Normal^^: the supporting force a surface exerts on objects in contact with it (to keep the object from falling through).
- Perpendicular to the surface.
- Any lifting force on an object will reduce the normal force and vice versa.
- ^^Tension^^: the pulling force of a cable holding up another object.
- Always points away from the hanging object.
- On an ideal pulley, the tension on both sides of the wheel are the same.
- ==At-a-distance/non-contact forces==: forces that don’t require physical contact
- ^^Gravitational^^: attractive force between masses.
- Electrical: attractive force between an electron and a nucleus.
- Magnetic: attractive force between opposite poles and repelling force between similar poles.
- Electrical and magnetic forces concern AP Physics 2 students
Newton’s Laws of Motion
- An object at rest/motion stays that way unless acted upon a net external force.
- If the net force (sum of all forces acting on an object) = 0, the object’s (lack of) motion will not change.
- This property is often referred to as inertia.
- Mass is the measure of inertia and is directly proportional to it. (more mass = more inertia)
- Acceleration is directly proportional to the net force applied on an object, but is inversely proportional to mass.
- ΣF = ma → divide both sides by mass → a = ΣF/m
- Every applied force will have an equal and opposite reaction.
- These forces don’t cancel out because they get applied on different objects.
- Example: hand pushes a wall, wall pushes back on hand with equal force
Force Equations
- Force = F = ma
- On a ramp of angle θ, F = mgsinθ
- Normal force = N = W = mg
- Elevators: N = W + Fₑ = mg + ma = m(g + a)
- On a ramp of angle θ, N = mgcosθ
- Friction = ƒ = μN
- Gravitational force = F₉ = Gm₁m₂/r²
- r = distance between the two masses
Solving Force Problems
Forces Only
- Read the question.
- Draw a diagram showing all the forces acting on the object (no components).
- Based on the diagram and the situation, decide if the net force equals 0 or not. Then write the statement ΣF = ma or ΣF = 0.
- Replace ΣF with all of the given/implied forces involved in the problem.
- Expand the forces if possible (e.g w = weight = mg).
- Isolate the variable you are solving for.
- Input values.
Force-Kinematics Problems
- Follow steps 1-4 above.
- List all kinematics variables you know based on the question.
- Solve for acceleration using forces or kinematics depending on which on you are given enough info for. This is because both the force equation and most kinematics equations contain acceleration.
- Substitute into the other equation and solve.