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# Newton's First and Second Laws

## Define force and Newton, and calculate using Newton's Second Law

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Newton’s First and Second Laws of Motion

Credit: CK-12 Foundation

This image is of Buzz Aldrin, one of the first men to walk on the moon.  Apollo 11 was the spaceflight that landed the first humans, Neil Armstrong and Buzz Aldrin, on the Moon on July 20, 1969.  Armstrong became the first to step onto the lunar surface 6 hours later on July 21.

This accomplishment could not have occurred without a thorough understanding of physics.

### Newton’s First and Second Laws of Motion

What is a force?  A force can be defined as a push or pull.  When you place a book on a table, the book pushes downward on the table and the table pushes upward on the book.  The two forces are equal and there is no resulting motion of the book.  If, on the other hand, you drop the book, it will fall to the ground pulled by a force called gravity.

If you slide a book across the floor, it will experience a force of friction which acts in the opposite direction of the motion.  This force will slow down the motion of the book and eventually bring it to rest.  If the floor is smoother, the force of friction will be less and the book will slide further before coming to rest.  If a perfectly smooth floor could be created, there would be no friction and the book would slide forever at constant speed.

Newton’s First Law of Motion describes an object moving with constant speed in a straight line.  In the absence of any force, the object will continue to move at the constant speed.  If the object is at rest, in the absence of any force, it will remain at rest.  Newton’s First Law states that an object with no force acting on it moves with constant velocity.  (The constant velocity could, of course, be 0 m/s.)

If the object suffers two opposing forces, the motion of the object is determined by the net force.  A more careful expression of Newton’s First Law is "an object with no net force acting on it remains at rest or moves with constant velocity in a straight line."

The statement above is equivalent to a statement that "if there is no net force on an object, there will be no acceleration."  In the absence of acceleration, an object will remain at rest or will move with constant velocity in a straight line.  The acceleration of an object is the result of an unbalanced force.  The magnitude of the acceleration is directly proportional to the magnitude of the unbalanced force.  The direction of the acceleration is the same direction as the direction of the unbalanced force.  The magnitude of the acceleration is inversely proportional to the mass of the object.  i.e.  The more massive the object, the smaller will be the acceleration produced by the same force.

These relationships are stated in Newton’s Second Law of Motion, "the acceleration of an object is directly proportional to the net force on the object and inversely proportional to the mass of the object."

Newton’s Second Law can be summarized in an equation.

a=Fm or more commonly, F=ma\begin{align*}a=\frac{F}{m} \ \text{or more commonly}, \ F=ma\end{align*}

According to Newton’s second law, a new force on an object causes it to accelerate and the larger the mass, the smaller the acceleration.  Sometimes, the word inertia is used to express the resistance of an object to acceleration.  Therefore, we say that a more massive object has greater inertia.

The units for force are defined by the equation for Newton’s second law.  Suppose we wish to express the force that will give a 1.00 kg object an acceleration of 1.00 m/s2.

F=ma=(1.00 kg)(1.00 m/s2)=1.00 kgm/s2\begin{align*}F = ma = (1.00 \ \text{kg})(1.00 \ \text{m/s}^2) = 1.00 \ \text{kg}\cdot\text{m/s}^2\end{align*}

This unit is defined as 1.00 Newton or 1.00 N.

kgms2=Newton\begin{align*}\frac{kg \cdot m}{s^2}=\text{Newton}\end{align*}

Example Problem:   What new force is required to accelerate a 2000. kg car at 2.000 m/s2?

Solution:  F=ma=(2000. kg)(2.000 m/s2)=4000. N\begin{align*}F = ma = (2000. \ \text{kg})(2.000 \ \text{m/s}^2) = 4000. \ \text{N}\end{align*}

Example Problem:  A net force of 150 N is exerted on a rock.  The has an acceleration of 20. m/s2.  What is the mass of the rock?

Solution:  m=Fa=(150 N)(20. m/s2)=7.5 kg\begin{align*}m = \frac{F}{a} = \frac{(150 \ \text{N})}{(20. \ \text{m/s}^2)} = 7.5 \ \text{kg}\end{align*}

Example Problem:  A net force of 100. N is exerted on a ball.  If the ball has a mass of 0.72 kg, what acceleration will it undergo?

Solution:  a=Fm=(100. N)(0.72 kg)=140 m/s2\begin{align*}a = \frac{F}{m} = \frac{(100. \ \text{N})}{(0.72 \ \text{kg})} = 140 \ \text{m/s}^2\end{align*}

#### Summary

• A force is a push or pull.
• Newton’s First Law states that an object with no net force acting on it remains at rest or moves with constant velocity in a straight line.
• Newton’s Second Law of Motion states that the acceleration of an object is directly proportional to the net force on the object and inversely proportional to the mass of the object.  Expressed as an equation, F=ma\begin{align*}F = ma\end{align*}.

#### Practice

Professor Mac explains Newton’s Second Law of Motion.

#### Review

1. The combined mass of a motorcycle and the rider is 275 kg. The cycle is slowing at a constant
rate of 4.5 m/s/s. What is the magnitude of the net force on the bike?

2. Calculate the average force that must be exerted on a 0.145 kg baseball in order to give it an acceleration of 130 m/s2.
3. A 1500-kg car is moving with an initial velocity of 20 m/s and comes to a stop in 5 seconds.
What is the size of the net force acting on the car?

4. A shot-putter exerts a net force of 140N on a shot. What is the mass of the shot if the shot
accelerates at 19 m/s2?

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