# Mechanics

calculus-based physics for scientists and engineers

## Newton's Third Law in 1D

### Newton's Third Law and Force Pairs

I'm not even going to post a definition of Newton's Third Law, because saying it concisely almost always is useless at best, if not misleading. Newton's Third Law helps describe how two objects interact with each other. It says that Newton's Third Law force pairs (N3FP) exist. What they are and how to find them are described in the video.

### Two Blocks

This is the best non-trivial example of Newton's Third Law. Really spend time with this one. If you fully understand Two Blocks you are a long way to mastering Newton's Third Law.

### Solution

1.

The video shows two masses, $$m_A = 40$$ kg and $$m_B = 5$$ kg. The ground is frictionless. There is a horizontal contact force (friction) on B by A providing an acceleration to the right of 4 m/s2. Mass A is accelerating to the right at 5 m/s2. What are the magnitudes of the frictional contact forces between the blocks and the tension in the string, T?

### Solution

2. A 1000 kg car is pushing a 4000 kg truck down the road to the right. The truck is rolling freely in neutral and experiences a frictional contact force from the ground directed to the left with a magnitude of 800 N. The car is in gear and experiences a frictional contact force from the earth of 7500 N to the right. What are the accelerations of the two vehicles and contact forces between them?

### Solution

3.

Bob (90 kg) is standing on a box (60ks) that is on the floor of an elevator (800 kg). A cable is accelerating the elevator up with a tension of 13,000 N. What is the acceleration of the system and the forces between all three objects?