IB Physics SL and HL · Theme A.2 · Part 1: Forces · by Ahmed Gomaa

Forces Field Guide

Forces in pictures. Pick a situation, drag the sliders and watch every force change: friction that grows until it gives up, a block that floats or sinks, a lift that makes you heavier, and pulleys that move.

Weight Normal force, tension, buoyancy Friction and drag Applied force Acceleration and net force

Part 1Seeing forcesSections 01–03

01Free-body diagrams

← Back to the notes: Free-body diagrams

A free-body diagram shows one body and every force on it. Each arrow starts at the body, points the way the force acts, and its length shows its size. For every arrow you must be able to name the other body that exerts it.

Exam trapThere is no "force of motion", no "force of the throw" after the ball leaves the hand, and no extra "centripetal force". If no other body exerts it, it is not a force.

02Third-law pairs

← Back to the notes: Newton’s third law

A book rests on a table. Two forces act on the book, and they balance. But they are not a third-law pair. Choose a force to see its real partner: the same type of force, equal in size, opposite in direction, acting on the other body.

03Equilibrium at an angle

← Back to the notes: Resultant force and equilibrium

A 120 N sign hangs from the middle of a cable. Only the vertical components of the two tensions hold it up: 2T sin θ = W. Make the cable flatter and watch the tension grow. The three forces always close into a triangle, because the resultant is zero.

cable angle θ

Angle θ—

Tension T—

T ÷ W—

Key ideaEquilibrium means ΣF_x = 0 and ΣF_y = 0. A cable can never be perfectly straight under a load: as θ → 0, T → ∞.

Part 2Friction and fluidsSections 04–06

04Static and sliding friction

← Back to the notes: Friction

A 40 kg crate rests on a floor with μ_s = 0.50 and μ_d = 0.35. Increase the push from zero. Static friction matches the push exactly, until it reaches its limit μ_sF_N = 196 N. Then the crate slides and friction drops to μ_dF_N = 137 N.

push F

Push—

Friction—

Acceleration—

Exam trapμ_sF_N is the largest static friction, not the friction on every body at rest. A crate pushed with 120 N has a friction force of 120 N.

05Float or sink?

← Back to the notes: Buoyancy (upthrust)

A 10 cm cube (volume 1.0 × 10⁻³ m³) is put in a liquid. Its weight depends on its own density; the largest buoyancy ρ_fluidVg depends only on the liquid. Change the densities: a floating cube sinks just deep enough for buoyancy to equal its weight.

density of the cube

Weight—

Buoyancy—

Fraction under the surface—

Push from the tank floor—

Key ideaF_b = ρ_fluidV_displacedg. Floating: fraction under the surface = ρ_body/ρ_fluid. Try the mercury: even steel (7800 kg m⁻³) would float on it.

06Terminal speed in a liquid

← Back to the notes: Terminal speed in a fluid

A steel sphere (7800 kg m⁻³) is released in a liquid of density 1260 kg m⁻³. Buoyancy acts from the start; drag 6πηrv grows with speed. Move the time slider to watch the forces change, and the radius and viscosity sliders to change the terminal speed.

radius r viscosity η time (in units of τ)

Terminal speed—

Starting acceleration—

Time constant τ—

Speed now—

weight = buoyancy + drag → v_t = 2r²g(ρ_s − ρ_f) / 9η

Exam trapThe starting acceleration is less than g in a liquid, because buoyancy acts at once. And for small spheres in thick liquids the terminal speed is reached in milliseconds.

Part 3Newton's second law in actionSections 07–11

07Lift and apparent weight

← Back to the notes: Lifts and apparent weight

A 60 kg student stands on a scale in a lift. The scale reads the normal force, F_N = m(g + a), with up positive. Only the acceleration matters, not the direction of motion.

acceleration a (up +)

Scale reading—

As a "mass" on the scale—

Compared with the weight—

08The slope

← Back to the notes: The inclined plane

A 5.0 kg block is placed at rest on a slope. Split the weight into mg sin θ down the slope and mg cos θ into it. The block stays put while mg sin θ ≤ μ_smg cos θ, that is while tan θ ≤ μ_s.

angle θ μ_s μ_d

mg sin θ (down the slope)—

Largest static friction—

Acceleration—

Slipping angle (tan θ = μ_s)—

09Connected objects

← Back to the notes: Connected bodies

Two objects joined by a string, or pushing on each other, move with the same acceleration. Treat them as one body to find a, then take one body on its own to find the force between them. Choose a set-up and change the masses and the force.

rear block m₁ front block m₂ force F μ_d (both blocks)

Acceleration (whole system)—

Force between the objects—

Share of F—

Key ideaThe force between the objects only has to accelerate the object(s) it pulls or pushes. With no friction (or the same μ for both), the string tension is T = F × m_pulled / (m₁ + m₂): it never equals F.

Exam trapPutting F on both objects. F acts only on the object it touches. The other object feels only the string tension or the contact force.

10Pulleys

← Back to the notes: Pulleys: the two set-ups

Two set-ups you must know. Change the masses and the friction, then press Release. The tension is the same on both sides of a light, smooth pulley, and it is never equal to the weight of a mass that accelerates.

block on table M hanging mass m μ_s μ_d

t = 0.0 s

Acceleration—

Tension—

Weight of hanging mass—

The method

Mark the direction each body moves: that is its positive direction.
Write ΣF = ma for each body, with the same T.
Add the equations: T cancels and gives a. Put a back to get T.

11Stacked blocks

← Back to the notes: One block on another

A block rests on another block on a smooth floor; a force F pulls the bottom block. Only friction can drag the top block along, and it has a limit μ_sm_topg. Increase F until the blocks start to slide over each other.

pull F top mass bottom mass μ_s μ_d

Largest F for moving together—

Friction between the blocks—

Acceleration of top block—

Acceleration of bottom block—

Key ideaTogether: F_max = (m_top + m_bottom) μ_sg. Sliding: use μ_d and write F = ma for each block on its own.

12Practice and self-check

Answers checked by calculation. Use g = 9.8 m s⁻². Try each one before you open it.

1. A 25 kg crate is pushed with 80 N. μ_s = 0.40 and μ_d = 0.30. Does it move? What is the friction force?

Largest static friction = 0.40 × 25 × 9.8 = 98 N. 80 N < 98 N, so it does not move and friction = 80 N.

2. A plastic block of density 900 kg m⁻³ floats in sea water of density 1030 kg m⁻³. What fraction is under the surface?

Fraction = 900/1030 = 0.87 (87 %).

3. The radius of a sphere falling at terminal speed in oil is tripled. By what factor does the terminal speed change?

v_t ∝ r², so it becomes 9 times larger.

4. A 70 kg man stands on a scale in a lift moving down and slowing at 1.5 m s⁻². Find the reading.

Slowing while moving down → acceleration upwards. F_N = 70(9.8 + 1.5) = 791 N (about 790 N).

5. A block just starts to slide when a slope is tilted to 31°. Find μ_s.

μ_s = tan 31° = 0.60.

6. Masses of 1.5 kg and 2.5 kg hang over a smooth pulley. Find the acceleration and the tension.

a = (2.5 − 1.5) × 9.8/4.0 = 2.45 m s⁻². T = 2 × 2.5 × 1.5 × 9.8/4.0 = 18.4 N (between 14.7 N and 24.5 N ✓).

7. A 2.0 kg block sits on a 6.0 kg block on a smooth floor; μ_s = 0.30 between them. Find the largest force on the bottom block for which they move together.

Top block: a_max = μ_sg = 2.94 m s⁻². F = 8.0 × 2.94 = 23.5 N.

8. A lamp hangs from a cable whose two halves each make 10° with the horizontal. Its weight is 50 N. Find the tension.

T = 50/(2 sin 10°) = 144 N, almost three times the weight.

Before the exam, can you…

draw a correct free-body diagram for any body?
name the third-law partner of any force?
solve equilibrium problems with components?
tell static friction from its maximum value?
explain buoyancy with pressure, and use F_b = ρVg?
say when Stokes' law applies, and derive v_t?
find the scale reading in an accelerating lift?
split the weight on a slope and decide if a block slips?
find the tension or contact force between connected objects?
solve both pulley set-ups for a and T?
find the largest force for stacked blocks to move together?