Applications of Newton's Laws: Pulleys and Systems

Active learning works for pulleys and connected systems because students often struggle to visualize forces across multiple objects at once. Moving, measuring, and discussing real systems makes the abstract concrete, helping students see how shared variables like tension and acceleration tie the equations together.

• 12th Grade
• Physics
• 3 activities
• 40 min–60 min

Learning Objectives

1. Calculate the acceleration of a system of two or more connected objects, including those interacting with pulleys, using Newton's Second Law.
2. Analyze the tension forces transmitted through ropes and massless pulleys in a connected system by drawing and applying free-body diagrams.
3. Design a simple pulley system to lift a specified mass with a target applied force, justifying the pulley configuration based on mechanical advantage principles.
4. Compare the net force and acceleration of individual objects within a connected system to the overall system's motion.

Peer Teaching

⏱ 40 min·Pairs

Peer Teaching: The Atwood Machine Analysis

Pairs work through an Atwood machine (two masses over a pulley). One student sets up free-body diagrams and writes Newton's Second Law for each mass; the other explains the tension and acceleration relationships. They swap roles for a different mass configuration and compare predictions to measured accelerations.

Prepare & details

Analyze how tension forces are transmitted through ropes and pulleys in a system.

Facilitation Tip: During the Atwood Machine Analysis, circulate and ask groups to explain how their free-body diagrams connect through the same tension and acceleration values.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Inquiry Circle

⏱ 60 min·Small Groups

Inquiry Circle: Mechanical Advantage Pulley Lab

Groups build simple and compound pulley systems using ring stands and spring scales. They measure the force required to lift a given weight with each configuration, calculate the mechanical advantage, and explain what trade-off (pulling distance) compensates for the reduced force needed.

Prepare & details

Predict the acceleration of a multi-object system using free-body diagrams and Newton's Second Law.

Facilitation Tip: In the Mechanical Advantage Pulley Lab, ensure students measure forces with spring scales only when the system is in equilibrium to avoid dynamic errors.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Gallery Walk

⏱ 45 min·Small Groups

Gallery Walk: Connected System Problem Sets

Post 6 different connected-object scenarios around the room (two masses over a pulley, a block on a ramp connected to a hanging mass, etc.). Groups rotate and write the system equations for each scenario without solving, then reconvene to solve one problem collectively as a class.

Prepare & details

Design a system of pulleys to lift a heavy object with a reduced applied force.

Facilitation Tip: For the Gallery Walk, require students to annotate their problem sets with clear labels for tension and acceleration before sharing with peers.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Teaching This Topic

Experienced teachers approach this topic by having students work in small groups to solve scaffolded problems first, then gradually increasing complexity. Avoid giving away solutions too quickly, as the process of setting up simultaneous equations is the core skill. Research suggests that whiteboarding solutions in front of the class helps students see the connections between their peers’ reasoning and their own.

What to Expect

Successful learning looks like students correctly drawing separate free-body diagrams for each object, writing Newton’s Second Law for each, and solving the resulting system of equations. Students should also explain how tension and acceleration connect the objects in their analysis.

Watch Out for These Misconceptions

Common Misconception

During the Atwood Machine Analysis, watch for students who think tension changes as it passes over the pulley.

What to Teach Instead

Have students use two spring scales on either side of the pulley in the lab setup and observe that they read the same force in equilibrium. Ask them to explain why this confirms tension is uniform in an ideal rope.

Common Misconception

During the Mechanical Advantage Pulley Lab, watch for students who believe both objects in a connected system experience the same net force.

What to Teach Instead

Direct students to draw separate free-body diagrams for each mass and write Newton’s Second Law for both. Ask them to compare the net force expressions and discuss why they differ despite the shared acceleration.

Assessment Ideas

Quick Check

During the Atwood Machine Analysis, collect students’ free-body diagrams and Newton’s Second Law equations for two connected blocks over a single fixed pulley. Check that they identify the common tension and acceleration variables and set up the equations correctly.

Exit Ticket

After the Mechanical Advantage Pulley Lab, present a scenario with a movable pulley lifting a 10 kg mass. Ask students to calculate the minimum applied force required to lift the mass at constant velocity, assuming an ideal pulley system, and explain their reasoning.

Discussion Prompt

After the Gallery Walk, pose the question: 'How does adding a second, identical block to the system described in the quick-check activity change the acceleration and the tension in the connecting string? Ask students to use their free-body diagrams and Newton’s Laws to justify their answers in small groups.

Extensions & Scaffolding

• Challenge: Provide a problem with three connected objects and ask students to calculate the required mass of a third object to achieve a specific acceleration.
• Scaffolding: Give students a template with pre-labeled free-body diagrams and partially completed Newton’s Second Law equations.
• Deeper exploration: Ask students to design their own pulley system to lift a given load with the least applied force, then test it in the lab.

Key Vocabulary

Tension	The pulling force transmitted axially by the means of a string, cable, chain, or similar one-dimensional continuous object.
Free-body diagram	A diagram showing all the forces acting on a single object, used to analyze its motion according to Newton's Laws.
Massless pulley	An idealized pulley with no mass, meaning it does not add to the inertia of the system and only redirects the tension force.
Mechanical Advantage	The ratio of the output force to the input force in a machine, indicating how much the machine multiplies the applied force.