Some Particular Forces — Question 1

Question 1

Weight is a gravitational force; a scale measures support

A 6 kg block rests on a horizontal force scale in an inertial room. Take $g=10$ m/s$^2$. No other vertical forces act.

1. Find Earth’s force on the block and the scale’s normal force on it.

2. Which interaction determines the force-scale reading?

3. If the entire block-scale assembly falls freely and loses compression, what happens to weight and reading?

Question 1 - Solution

Weight is a gravitational force; a scale measures support

(a) Balance the resting block.

$$W=mg=6(10)=60\,\mathrm N,\quad N-W=0\ \Rightarrow\ \boxed{N=60\,\mathrm N}$$ Weight is 60 N downward. Since $a_y=0$, the scale force is 60 N upward.

(b) Identify what the sensor senses.

$$R_{\mathrm{scale}}=N,\quad N=m(g+a_y)\quad\text{while contact persists}$$ The force scale measures contact compression, hence the normal-force magnitude N. In this stationary situation N equals mg, but the two forces have different agents.

(c) Remove the support interaction.

$$a_y=-g\ \Rightarrow\ N=m(g-g)=0,\quad W=mg=60\,\mathrm N$$ In ideal free fall the normal force is zero and the reading vanishes. Earth’s force remains 60 N downward under the stated constant-g model. Zero apparent weight does not imply zero gravitational attraction.