AP Physics 1 · Unit 2 · Topic 7 of 9 · 6 min lesson

Systems of Objects

A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.

Quiz this topic · 4 questions Watch the review video ↗

The big idea

For objects that move together, treat them as one system: the acceleration is the external net force divided by the total mass. Then look at one object alone to find a force between them, like tension or a contact push.

1. One system, then one object

The string makes both blocks move together, with the same size acceleration.

a = F_{net, external} ÷ m_totalwhole system

Internal forcescancel: leave them out

F_net = maone object: finds tension or contact force

2. Why internal forces drop out

Inside the system, the string pulls the 4 kg block forward and pulls the 1 kg block up. Those tensions are internal: they pull parts of the system against each other, so they don’t change how the whole system speeds up.

Only external forces go on the system’s free-body diagram: here, the 1 kg block’s weight is what drives everything.

Once you know a, isolate one object. Its free-body diagram does include the string or contact force, and F_net = ma tells you how big it is.

3. Example, then try it

Example

A 30 N force pulls a 4 kg cart, which tows a 2 kg cart behind it on a string. Frictionless track. Find the acceleration and the string tension.

System: a = 30 N ÷ 6 kg = 5 m/s².

Rear cart alone: the string is the only horizontal force on it, so F_T = (2 kg)(5 m/s²) = 10 N.

Try it · work it on paper first

In the figure below, find the acceleration and the string tension. (g = 10 m/s²)

External driving force: the hanging block’s weight, (1 kg)(10 N/kg) = 10 N. The table is frictionless.

System: a = 10 N ÷ (4 + 1) kg = 2 m/s².

Table block alone: the string is the only horizontal force, so F_T = (4 kg)(2 m/s²) = 8 N.

Check with the hanging block: mg − F_T = ma → 10 − 8 = (1)(2). ✓

Answer: a = 2 m/s²; tension = 8 N, less than the hanging block’s 10 N weight.

4. Common mistakes

Counting internal forces.Tension between two blocks of the system doesn’t go in the system’s net force.

“Tension equals the hanging weight.”Only if nothing accelerates. Here the hanging block speeds up, so the tension must be less than its weight.

Dividing by one mass.For the whole system, divide by the total mass of everything that moves together.

Check yourself

Two carts on a frictionless track are joined by a string. A 12 N force pulls the 3 kg front cart; the rear cart is 1 kg. What is the tension in the string?

System: a = 12 N ÷ 4 kg = 3 m/s². The string is the only horizontal force on the 1 kg rear cart, so F_T = (1 kg)(3 m/s²) = 3 N.

Ready to practice?

4 questions on Systems of Objects, each with a hint and an explanation for every wrong answer.

Quiz this topic All of Unit 2