Newton's First Law — Question 2

Question 2

Balanced forces allow either rest or steady motion

A box is subject to 12 N east and 12 N west horizontally; its vertical forces also balance. Consider one run initially at rest and another initially moving west at 2 m/s.

1. Find the horizontal net force.

2. Predict each run’s displacement after 5 s.

3. Can a force inventory with zero resultant determine the initial velocity?

Question 2 - Solution

Balanced forces allow either rest or steady motion

(a) Add signed forces.

$$\boxed{F_{{\mathrm{net}},x}=12-12=0\,\mathrm N},\quad a_x=0$$ With east positive, $F_{\mathrm{net},x}=12-12=0$ N. The full resultant is zero.

(b) Preserve each initial velocity.

$$\Delta x_A=0(5)=0,\quad\Delta x_B=(-2)(5)=-10\,\mathrm m$$ The resting run remains at its starting point. The moving run displaces 10 m west in 5 s. Both satisfy the same balanced-force condition.

(c) Supply the missing initial state.

$$\dot v=0\ \Rightarrow\ v(t)=C,\quad C=v(0)$$ The first law specifies that velocity remains constant when net force vanishes. It does not assign the value of that constant. An initial motion measurement is required.