Answer to Question #175423 in Physics for Maddy

Question

You are pushing a mobile imaging machine along a busy hospital corridor at a steady velocity of 1.31 m/s east. The machine’s mass is 23.1 kg. You see an obstacle 65 cm in front of your machine. What is the minimum braking force you must apply to the machine in order to stop the machine just before it hits the obstacle? (Assume you have instantaneous reaction time and that you will be able to apply a steady force for the full distance of the machine’s motion once you apply it.)

Answer 1

Let's first find the deceleration of the mobile imaging machine:

$$v^2=v_0^2+2as,$$ $$0=v_0^2+2as,$$ $$a=\dfrac{-v_0^2}{2s}=\dfrac{-(1.31\ \dfrac{m}{s})^2}{2\cdot0.65\ m}=-1.32\ \dfrac{m}{s^2}.$$

Finally, we can find the minimum braking force from the Newton's Second Law of Motion:

$$F_{braking}=ma=23.1\ kg\cdot(-1.32\ \dfrac{m}{s^2})=-30.5\ N.$$

The sign minus means that the braking force directed in the opposite direction to the motion of the mobile imaging machine.