Question

question #5
galileo conducted an experiment in which he rolled different balls down an inclined plane. he determined that each ball traveled a distance that was directly proportional to the square of the time it traveled. what did galileo conclude from this experiment?
a air resistance affects all objects equally.
b all objects accelerate toward earth at the same rate.
c objects with greater mass accelerate toward earth faster than less massive objects.
d the force of friction from the inclined plane causes a decrease in the acceleration of an object.

Explanation:

Galileo's inclined - plane experiment was a precursor to understanding free - fall. By showing that distance \(d\propto t^{2}\) (from the kinematic equation \(d = v_{0}t+\frac{1}{2}at^{2}\), with \(v_{0} = 0\) for starting from rest, \(d=\frac{1}{2}at^{2}\)), and since the same proportionality held for different balls (of different masses), it implied that the acceleration \(a\) was the same for all objects. This led to the conclusion that all objects accelerate toward Earth at the same rate (in the absence of air resistance, which was approximated in the inclined - plane experiment by reducing the effective acceleration due to gravity and thus minimizing the effect of air resistance relative to the motion).

• Option A: Air resistance was not the focus of this experiment. The inclined - plane experiment was more about the relationship between distance and time (and thus acceleration) for objects in motion under gravity - like influence (reduced by the incline).
• Option C: Contradicts Galileo's findings. If mass affected acceleration, the proportionality \(d\propto t^{2}\) (which implies a constant acceleration \(a\) from \(d=\frac{1}{2}at^{2}\)) would not hold for different - mass balls.
• Option D: While friction is a factor in real - world inclined - plane experiments, the key conclusion from the proportionality \(d\propto t^{2}\) was about the acceleration of objects due to gravity (or the component of gravity along the incline), not about the effect of friction. The experiment was designed to study the motion under an approximately constant force (component of gravitational force along the incline) and its relation to time and distance.

Answer:

B. All objects accelerate toward Earth at the same rate.