Newton’s Second Law of Motion

Claimed by Rahul Singi Fall 2016

History

Insert History

Main Idea

A Mathematical Model

At the most basic level, Newton's Second Law of Motion states that force is equal to mass multiplied by acceleration, or F=ma. At face value, this means the force applied on an object is dependent on only two factors, the mass of the object and the acceleration, or change of momentum of the object. However, Newton's Second Law of Motion provides us with more information than simply that. First, it shows that the force applied on an object must be in the same direction as the acceleration, as mass is simply a positive constant. This can be further investigated to show that the force increases as the magnitude of acceleration increases, meaning acceleration, momentum, and force all have a positive relationship.

Additionally, this law can be re-written to show that [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where dp/dt represents change of momentum. Therefore, the greater the change in momentum, the greater the force being applied on the object.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Manipulate the code to see the different motions of the cart. See what changing the direction of the force, the net force, or the mass of the ball does to the momentum and final position of the cart.

Example Problems

Simple

Given a object has a mass of 3.5 kg and an acceleration of 2.3 m/s^2. What is the force applied on the object?

Answer: 8.05 N

Explanation: Simply use the formula stated in Newton's Second Law of Motion. Force= 3.5(2.3)= 8.05 N

Middling

A car has a mass of 200 kg. The car starts at rest. Ten seconds later, the car is moving at a speed of 20 km/s. What is the force applied on the object?

Answer: 400 N

Explanation: First, solve for the acceleration by finding the change in velocity, over the change in time. Therefore (20-0)/(10-0)=20/10=2 m/^2. Then use this acceleration value and the given mass to implement Newton's Second Law of Motion. Therefore, Force= 200(2)=400 N

Connection to Newton's Other Laws

Insert

External Links

Insert

References

Insert