Some Particular Forces — Question 2

Question 2

An upward acceleration increases a floor scale reading

A 50 kg passenger stands on a horizontal scale in an elevator accelerating upward at 2 m/s$^2$. Take $g=10$ m/s$^2$.

1. Find the normal force and scale reading.

2. Would the answer change if the elevator were moving downward while accelerating upward?

3. Compare a constant-speed upward trip.

Question 2 - Solution

An upward acceleration increases a floor scale reading

(a) Apply the vertical force equation.

$$N-mg=ma_y\ \Rightarrow\ \boxed{N=m(g+a_y)=50(10+2)=600\,\mathrm N}$$ With upward positive, $N-mg=ma$, so $N=50(10+2)=600$ N.

(b) Use acceleration, not velocity.

$$N(v_y<0,a_y=+2)=N(v_y>0,a_y=+2)=600\,\mathrm N$$ No. The same upward acceleration gives the same 600 N reading even while the elevator moves downward and slows.

(c) Set acceleration to zero.

$$v_y=\text{constant}\ \Rightarrow\ a_y=0,\quad N=50(10)=500\,\mathrm N$$ At constant speed, $N=mg=500$ N. The direction or magnitude of a constant velocity does not alter this vertical balance.