Question

At the moment the acceleration of the blue ball is 9.40 m/s2, what is the ratio of the magnitudes of the force of air resistance to the force of gravity acting on the blue ball? use 9.81 m/s2 for the standard value of g at the location of the experiment.

Answer 1

Let us see. We have that Newton's Law holds in this case, so $\sum{F}=m*a$ where a is the acceleration of the ball, F the forces acting on it and m its mass. There are 2 forces acting on it, the force of gravity W and air resistance R. We can easily see that these two act in opposite directions (gravity towards the ground, resistance upwards), so |ΣF|=W-R (1) . We have that W=m*g where g=9.81 m/s2. We also have that ΣF=9.40*m. From this relationship, substituting into (1) all the known values, we get that R=m(9.81*-9.40)=m*0,41. We take then the ratio R/W. This is equal to:$\frac{0.41 m }{9.81m} =0.042=4.2\%$. This is our final answer.