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Mechanics Practice (Interactive)

Intuition

Physics practice is like learning a musical instrument — you must play (solve problems) to develop fluency, not just read sheet music (study formulas): The key to mechanics problems is translating physical scenarios into mathematical equations, then solving and interpreting the results

Why it matters: Regular practice builds the intuition needed to tackle unfamiliar problems in exams and real-world applications

The key insight: The key to mechanics problems is translating physical scenarios into mathematical equations, then solving and interpreting the results

IB Physics — Mechanics Practice

8 auto-graded practice problems at medium to hard difficulty, aligned to the IB Physics syllabus (SL/HL). Select an answer, submit, and review the explanation.

Worked Examples

Example 1: Inclined Plane with Friction

Problem: A 2.0 kg block slides down a 35° incline with μk=0.25\mu_k = 0.25. Find the acceleration. (g=9.81g = 9.81 m/s²)

Solution: Step 1: Component of gravity along incline: mgsin⁡35°=2.0×9.81×0.574=11.26mg\sin 35° = 2.0 \times 9.81 \times 0.574 = 11.26 N

Step 2: Normal force: N=mgcos⁡35°=2.0×9.81×0.819=16.07N = mg\cos 35° = 2.0 \times 9.81 \times 0.819 = 16.07 N

Step 3: Friction force: f=μkN=0.25×16.07=4.02f = \mu_k N = 0.25 \times 16.07 = 4.02 N

Step 4: Net force along incline: Fnet=11.26−4.02=7.24F_{net} = 11.26 - 4.02 = 7.24 N

Step 5: a=Fnetm=7.242.0=3.62a = \frac{F_{net}}{m} = \frac{7.24}{2.0} = 3.62 m/s²

Key insight: Always resolve forces along and perpendicular to the incline, not horizontally and vertically.

Example 2: Work-Energy Theorem

Problem: A 5.0 kg object slides across a rough surface with μk=0.30\mu_k = 0.30. If it starts at 10 m/s, how far does it slide before stopping?

Solution: Step 1: Work-energy theorem: Wnet=ΔKEW_{net} = \Delta KE

Step 2: Work done by friction: W=−f×d=−μkmg×dW = -f \times d = -\mu_k mg \times d

Step 3: ΔKE=0−12mv2=−12(5.0)(10)2=−250\Delta KE = 0 - \frac{1}{2}mv^2 = -\frac{1}{2}(5.0)(10)^2 = -250 J

Step 4: −0.30×5.0×9.81×d=−250-0.30 \times 5.0 \times 9.81 \times d = -250

Step 5: d=25014.715=17.0d = \frac{250}{14.715} = 17.0 m

Key insight: Work-energy problems are often easier than using F=maF = ma because you don’t need to find time or acceleration first.

Example 3: Projectile from Height

Problem: A ball is thrown at 25 m/s at 30° above horizontal from a 20 m building. Find the time of flight. (g=9.81g = 9.81 m/s²)

Solution: Step 1: Vertical component: uy=25sin⁡30°=12.5u_y = 25\sin 30° = 12.5 m/s

Step 2: When the ball hits the ground, s=−20s = -20 m (below starting point)

Step 3: Use s=uyt−12gt2s = u_y t - \frac{1}{2}gt^2: −20=12.5t−4.905t2-20 = 12.5t - 4.905t^2

Step 4: 4.905t2−12.5t−20=04.905t^2 - 12.5t - 20 = 0

Step 5: t=12.5±156.25+392.49.81=12.5±23.429.81t = \frac{12.5 \pm \sqrt{156.25 + 392.4}}{9.81} = \frac{12.5 \pm 23.42}{9.81}

Step 6: t=35.929.81=3.66t = \frac{35.92}{9.81} = 3.66 s (reject negative root)

Key insight: For projectiles from heights, the displacement is negative when the landing point is below the starting point.

Kinematics

Dynamics

Energy

Momentum

Common Mistakes

Confusing elastic with perfectly inelastic collisions: Elastic collisions conserve both momentum AND kinetic energy. Perfectly inelastic collisions conserve momentum but stick together (maximum KE loss). Don’t assume all collisions are elastic.

Forgetting to define a sign convention: Always specify which direction is positive before solving momentum problems. Mixing up signs is the most common error.

Mixing up impulse with force: Impulse is force × time (Ns). Force is impulse/time (N). They’re related but different quantities.

Cross-References

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.