Chapter 6, Problem 71A

Write a letter to a friend who has not yet studied physics and tell what you've learned about Galileo introducing the concepts of acceleration and inertia. Tell of how Galileo was also familiar with forces, but didn’t see the connection among these three concepts. Tell how Isaac Newton did see the connection, revealed in his second law of motion. Explain with the second law why heavy and light objects in free fall gain the same speed in the same time. In this letter, it’s okay to use an equation or two, making it clear that you see equations as a shorthand notation of explanations.

To determine

To Explain: The connection between the Force, acceleration and inertia, Newton’s second law and the way heavy and light objects gain same speed in free falls.

Explanation of Solution

Introduction:

Inertia is the property or can say tendency of a body to be in the rest position unless any force acts on it.More is the mass, more is the inertia to the body.

Acceleration is the rate of change of velocity with respect to time.

Force is the product of mass and acceleration.

Galileowas aware of the concept of inertia, acceleration and force but he couldn’t find out the relationship between these quantities, which were later explained by Newton.

According to Newton’s second law of motion, product of mass and rate of change of velocity is equal to the force acting on the body.

  $m\times \frac{dv}{dt}=F$

Where,

m is the mass of body

  $\frac{dv}{dt}$ is the acceleration

F is the force acting on the body.

Mass of the body is related to inertia.

The above equation gives relationship between Force, acceleration and inertia.

Free fall is the motion of an object when no other forces except for gravity act on it. There is no air resistance offered to the falling object. No speed dissipative forces act on the object. When two objects, one is heavier and another is lighter experience a free fall, then both the objects would reach the ground at the same time, because the gravity acting on both bodies is same. So they would have same acceleration and hence velocity. Hence, both objects will reach the ground at the same time.

Conclusion:

Gravitational pull is always same for all bodies but because of air resistance the lighter object cannot reach the ground early. In case of free fall, there are no dissipative forces. so,the objects will reach the ground at the same time with the same speed.