Question

In a vacuum, a 74 gram feather will fall to the Earth at the same rate (acceleration) as a 7.26 kg bowling ball. Which one will hit the ground first? Then use Newton’s 2nd Law of Motion to explain which object (the feather or the bowling ball) experiences a greater force due to gravity.

Answer 1

We know that both objects fall at with the same acceleration, let's define that acceleration as g = 9.8m/s^2

Then the acceleration of both objects will be:

A(t) = -9.8m/s^2

Where the minus sign is because the gravity pulls the objects down.

Now, to get the velocity of the objects, we integrate over time, and get:

V(t) = (-9.8m/s^2)*t + v0

Where V0 is the initial velocity of the objects, because we do not have information about this, we can assume that both objects have the same value of V0, so for now, the movement equations are the same for both of them

To get the position we integrate again over time and get:

P(t) = (1/2)*(-9.8m/s^2)*t^2 + v0*t + P0

Where P0 is the initial position and same as above, we can assume that is the same for both objects.

Then both objects have the same motion equations, and the mass does not appear in any of them, then we can conclude that they will hit the ground at exactly the same time, because their motion equations are exactly the same.

B) By Newton's second law we know that:

F = m*a

Force equals mass times acceleration.

We know that both objects suffer the same acceleration, 9.8m/s^2

Then the force for the feather will be:

(remember that 1kg = 1000g, then 74g = (74/1000) kg = 0.074kg)

F = 0.074kg*9.8m/s^2 = 0.7252 N

And for the bowling ball will be:

F = 7.26kg*9.8m/s^2 = 71.148 N

Then you can see that the bowling ball experiences a greater force.