Newton's Third Law — Question 4

Question 4

A sensor reads the tension, not the sum of opposite end pulls

A light sensor is stretched horizontally by two people, each pulling outward with 40 N. The sensor remains at rest and is calibrated to report its internal tensile load.

1. Find the net external force on the sensor.

2. Find the sensor reading.

3. Are the two people’s forces on the sensor a third-law pair?

Question 4 - Solution

A sensor reads the tension, not the sum of opposite end pulls

(a) Sum the external vectors.

$$\boxed{F_{{\mathrm{net}},x}=40-40=0\,\mathrm N}$$ With right positive, $40-40=0$ N. This explains its lack of translational acceleration.

(b) Identify the transmitted tensile load.

$$\text{One half:}\quad T-40=0\ \Rightarrow\ T=40\,\mathrm N$$ The reading is 40 N, not 80 N and not zero. A cut through the ideal light sensor transmits the 40 N tension needed to balance either end.

(c) Reverse each interaction separately.

$$\vec F_{L\to S}=-\vec F_{S\to L},\quad\vec F_{R\to S}=-\vec F_{S\to R}$$ Both end forces act on the sensor, so they are not a third-law pair with one another. Each is paired with the sensor’s opposite force on the corresponding person.