AP Physics 1 · Unit 2, Part 1 · Forces

Two-Body Systems Practice Problems

Connect force equations for objects joined by a rope. Practice Atwood machines, a cart pulled by a hanging load, friction, unknown masses, and a three-load extension.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Two-Body Systems lesson. — A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Choose the system, then connect the motion

Use the rope constraint

Relate the displacements and acceleration magnitudes of connected loads. Choose consistent positive directions along their motion.

Combine object equations

Add the force equations to find system acceleration, then isolate one object to solve for tension or an unknown mass.

Extend the model

Compare vertical Atwood systems with a cart and hanging load. Include rough-table friction, an angled winch force, and a third connected load.

A question from this set

One rope connects the motion

Two unequal loads hang from opposite ends of a taut, light rope over an ideal fixed pulley. When released, how do their acceleration magnitudes compare?

The heavier load has the larger acceleration magnitude.
The magnitudes are equal, and the loads accelerate in opposite directions.
The lighter load has the larger acceleration magnitude.

Try it in the practice set

A taut rope connects unequal loads over an ideal fixed pulley.

Key ideas

One connection creates related accelerations

A light taut rope constrains motion

For the ideal fixed-pulley setups, the two ends move equal distances in equal time. They can accelerate in opposite directions with the same magnitude.

Internal tension cancels in a system equation

When both connected objects are included, the rope’s internal forces cancel in the combined equation. A separate equation for either object still includes tension.

See the physics

Track both ends of the rope

Check your equations, then compare both objects’ changing velocities and travel distances. Reveal the tension after running and compare it with the weight and acceleration you used.

Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.

Ready for two-body systems?

Begin with a conceptual question, then work through the calculations.

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