Balanced or Unbalanced

Question

For each situation, determine whether the forces acting on a roller coaster are balanced or unbalanced and explain why using physics terms please:

 

• The roller coaster moves at a constant velocity as it ascends

 

• The roller coaster sits at rest at the top of the first hill

 

• The roller coaster accelerates toward the bottom of the hill at a rate of 9.8 m/s^2

 

• The roller coaster's brakes activate, causing it to decelerate

 

• The roller coaster slows to a stop at the end of the track

Answer 1

Newton's Second Law is the sum of all forces acting on a body equals its mass times acceleration, or

 

ΣF = ma

 

There is a subject called Statics. This is subject where we study situations where all of the forces in the problem are balanced. This means that the sum of the forces equals 0. This means that inertially, there is no acceleration.

 

- The roller coaster moves at a constant velocity as it ascends:

The acceleration is the rate of change of velocity. If the velocity is constant, then its time rate of change, or acceleration, is zero. So, this is balanced.

 

- The roller coaster sits at rest at the top of the first hill:

This is very much like the first problem. In the previous problem, the system was in dynamic equilibrium because it was moving at a constant velocity. In this system, the velocity is also constant, and it is specifically zero. Systems with no velocity are said to be in static equilibrium. So, this is also balanced

 

- The roller coaster accelerates toward the bottom of the hill at a rate of 9.8 m/s^2

There is specifically a nonzero acceleration called out here. So, this is unbalanced.

 

- The roller coaster's brakes activate, causing it to decelerate 

This problem shows a definite acceleration. This is a negative acceleration caused by the application of the brakes. So, this is also unbalanced.

 

- The roller coaster slows to a stop at the end of the track:

This is showing a change in velocity with respect to time, where the roller coaster's velocity approaches zero. A change in velocity with respect to time is an acceleration, specifically a deceleration. So, this is likewise unbalanced.