Physics Unit 2

Net force

The combined effect of all forces on an object, including their directions.

Newton's Second Law: Fnet = ma

Connects net force, mass, and acceleration. Use to find any one when you know the other two. Rearrange: a = Fnet/m; Fnet = ma; m = Fnet/a.

What does zero net force mean?

Acceleration is zero. The object is either at rest OR moving at constant velocity.

What direction does net force point?

In the direction of acceleration, not necessarily the direction of motion.

Forces in the same direction

Add their magnitudes.

Forces in opposite directions

Subtract the smaller magnitude from the larger; the net force points toward the larger force.

Weight / gravitational force: Fg = mg

Find the force of gravity on an object. Multiply mass in kg by g ≈ 9.8 m/s². Weight is measured in newtons.

Mass vs. weight

Mass is measured in kilograms and measures inertia. Weight is a gravitational force measured in newtons: Fg = mg.

Free-body diagram (FBD)

A diagram showing every external force acting ON one chosen object. Draw arrows in each force's direction and label them.

Normal force (FN)

The support force a surface exerts perpendicular to itself. It is not always equal to mg.

Book resting on a horizontal table

Vertical forces balance: FN = mg, provided there are no other vertical forces or acceleration.

Newton's First Law

An object maintains rest or constant velocity unless a nonzero net external force acts on it.

Newton's Third Law

For every force object A exerts on object B, B exerts an equal-magnitude, opposite-direction force on A.

Newton's Third Law: key trick

The two forces act on DIFFERENT objects, so they do not cancel on the same object's free-body diagram.

Applied force on a frictionless incline

If the block is at rest and the applied force is parallel uphill, it balances gravity's downhill component: Fapplied = mg sinθ.

Gravity parallel to an incline: mg sinθ

Find the component of gravity pulling an object down the ramp. Use when solving motion or force balance along the slope.

Gravity perpendicular to an incline: mg cosθ

Find the component of gravity pressing an object into the ramp. If no other perpendicular forces or acceleration exist, FN = mg cosθ.

Incline memory trick

SIN = slides down the slope; COS = presses into the surface. These are components of gravity, not separate forces.

Net force magnitude for perpendicular components

Fnet = √(Fx² + Fy²). Use when horizontal and vertical net-force components are perpendicular.

Net force angle: θ = tan⁻¹(Fy/Fx)

Find the angle relative to the horizontal when Fx is horizontal and Fy is vertical. Check the signs and the quadrant.

Constant velocity across a floor

Acceleration = 0, so net force = 0. If the box is sliding, applied force and friction balance if those are the only horizontal forces.

Elevator accelerating upward: N = m(g + a)

Find apparent weight/normal force when acceleration points upward. The normal force is greater than mg.

Elevator accelerating downward: N = m(g − a)

Find the normal force when acceleration points downward and a < g. The normal force is less than mg.

Elevator with zero acceleration: N = mg

Applies when the elevator is stationary OR moving at constant velocity.

Elevator formula tip

Use the direction of ACCELERATION, not the direction the elevator is traveling. Moving upward while slowing down means acceleration is downward.

Atwood machine acceleration: a = (mheavy − mlight)g/(mheavy + mlight)

Use for two hanging masses connected by a light string over an ideal frictionless pulley. The heavier mass goes down; the lighter mass goes up.

Atwood machine: why subtract the masses?

The difference in their weights drives the motion. Add both masses in the denominator because both masses accelerate.

Tension: what is it?

The pulling force transmitted by a taut string or rope. For an ideal massless string over a frictionless pulley, tension is the same on both sides.

Tension using a mass accelerating upward: T = m(g + a)

Use for a hanging mass accelerating upward. Tension must exceed its weight.

Tension using a mass accelerating downward: T = m(g − a)

Use for a hanging mass accelerating downward. Its weight exceeds the tension.

Tension in a block on a frictionless horizontal surface: T = ma

Use if tension is the only horizontal force on that block. Isolate the block and apply Newton's Second Law.

Connected blocks accelerating together

Treat them as one system to find acceleration: a = Fnet/(sum of masses). Then isolate one block to find tension or contact force.

Coefficient of friction (μ)

A unitless number describing how strongly two surfaces resist sliding. Larger μ means more friction for the same normal force.

Static friction

Friction that prevents surfaces from starting to slide relative to each other. It adjusts to the needed force up to a maximum.

Maximum static friction: fs,max = μs FN

Find the largest static friction possible, such as when an object is just about to move. Actual static friction can be smaller.

Kinetic friction: fk = μk FN

Find friction while surfaces are sliding relative to each other.

Static vs. kinetic friction

Static: before sliding. Kinetic: during sliding. Use the coefficient that matches the situation.

Normal force on a horizontal surface: FN = mg

Use when there is no vertical acceleration and no additional vertical forces. If other forces act vertically, re-evaluate FN.

Minimum horizontal force to start sliding: Fmin = μs mg

For a box on a horizontal surface with no other vertical forces, the required force reaches maximum static friction.

Friction on an incline

If a block tends to slide down, friction points uphill. If it tends to move up, friction points downhill.

Maximum incline angle before sliding: θmax = tan⁻¹(μs)

Use for a block on an incline just about to slip, assuming the standard model with gravity and static friction.

Incline acceleration sliding downward: a = g(sinθ − μk cosθ)

Use when a block slides down an incline with kinetic friction and no other forces along the slope. Positive result means downhill.

Incline with a hanging mass

Draw a separate FBD for each mass. Find gravity along the incline, normal force, and friction; then use Newton's Second Law for both masses with a consistent positive direction.

Kinematic equation: vf = vi + at

Find final velocity or acceleration/time when displacement is not needed.

Kinematic equation: Δx = vi t + ½at²

Find displacement when initial velocity, acceleration, and time are known.

Kinematic equation: vf² = vi² + 2aΔx

Connect velocity, acceleration, and displacement when time is not given.

Kinematic equation: Δx = [(vi + vf)/2]t

Find displacement using average velocity when acceleration is constant and initial/final velocities are known.

Kinematics symbols

vi = initial velocity; vf = final velocity; a = acceleration; t = time; Δx = displacement.

Choose a kinematic equation

List what is given and what you need. Choose an equation containing those quantities and as few unknowns as possible. These equations assume constant acceleration.

Friction-limited braking: |a| = μg

For a car braking on a level road at the maximum friction force, the deceleration magnitude is μg. Acceleration points opposite the motion.

Braking distance: vf² = vi² + 2aΔx

Use when solving how far an object travels while braking, especially when time is not given. For stopping, vf = 0.

Stopping distance with reaction time

Total = reaction distance + braking distance. Reaction distance = speed × reaction time; braking distance = vi²/(2|a|) when stopping with constant deceleration.

Reaction distance: d = vt

Distance traveled before braking begins. Use the car's speed and the driver's reaction time; convert units consistently.

Question asks for maximum static friction

Calculate μs FN. Do not assume that this amount is acting all the time.

Question says 'just starts moving'

The applied force has reached maximum static friction: Fapplied = fs,max, if horizontal forces are otherwise balanced.

Question says 'constant velocity'

Set net force equal to zero, even if the object is moving.

Question asks for acceleration of a connected system

Add the masses and use the net external force on the system. Internal tension forces cancel when considering the entire system.

Question asks for tension

Draw an FBD for one mass/block and apply Fnet = ma. Choose the object and sign convention carefully.

Question asks for force components on an incline

Resolve gravity into mg sinθ parallel to the ramp and mg cosθ perpendicular to the ramp.

Question asks for magnitude and direction of a 2D net force

Find net x and y components first. Use the Pythagorean theorem for magnitude and inverse tangent for angle.

Units to remember

Force: newtons (N). Mass: kilograms (kg). Acceleration: m/s². Speed: m/s. Time: seconds (s). Coefficient of friction: no units.

Reliable problem-solving routine

1) Draw the FBD. 2) Choose axes and positive directions. 3) Resolve angled forces if needed. 4) Write Fnet = ma for each axis/object. 5) Substitute values and check units and direction.