What happened to the division of g in the Mach 3 force diagram problem?

In summary, the conversation discusses an equation from a book that relates to a force diagram and the acceleration felt by a pilot. The confusion arises from the presence of g in the equation and its relation to the last term. The issue is resolved with clarification on the equation's equivalence.
  • #1
delve
34
0
Here is an answer from a book of mine: From the force diagram we have [tex]N-mg=(\frac{mv^2}{R})e_r[/tex]. The acceleration that the pilot feels is [tex]\frac{N}{m}=g+(\frac{mv^2}{R})e_r[/tex]. I'm confused though; what happened to the g being divided by the last term as well?
 
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  • #2
Hi delve! :smile:
delve said:
Here is an answer from a book of mine: From the force diagram we have [tex]N-mg=(\frac{mv^2}{R})e_r[/tex]. The acceleration that the pilot feels is [tex]\frac{N}{m}=g+(\frac{mv^2}{R})e_r[/tex]. I'm confused though; what happened to the g being divided by the last term as well?

I'm not following you …

the equation is equivalent to N/m = g + (v2/R)er

what do you mean by g being divided by something? :confused:
 
  • #3
Actually, you just helped me realize what I was confused about. Thank you!
 

What is a Mach 3 force diagram?

A Mach 3 force diagram is a visual representation of the forces acting on an object moving at Mach 3, which is three times the speed of sound. It shows the magnitude and direction of each force, as well as the resulting acceleration of the object.

Why is it important to use a Mach 3 force diagram?

Using a Mach 3 force diagram allows scientists and engineers to better understand and analyze the forces acting on an object at high speeds. It can help identify potential problems or design flaws, and guide the development of more efficient and safer technologies.

What are the main forces included in a Mach 3 force diagram?

The main forces included in a Mach 3 force diagram are thrust, drag, lift, and weight. Thrust is the force that propels the object forward, drag is the force that resists its motion, lift is the force that keeps it airborne, and weight is the force due to gravity pulling it downwards.

How do you calculate the forces in a Mach 3 force diagram?

The forces in a Mach 3 force diagram can be calculated using Newton's laws of motion. For example, thrust is calculated by multiplying the mass of the object by its acceleration, drag is calculated using the drag coefficient and the object's velocity, lift is calculated using the lift coefficient, and weight is calculated using the mass and acceleration due to gravity.

What are some real-world applications of Mach 3 force diagrams?

Mach 3 force diagrams are commonly used in the aerospace industry to design and test high-speed aircraft and spacecraft. They are also used in the development of hypersonic vehicles, such as missiles and high-speed trains. Additionally, they can be used in the analysis of natural phenomena, such as supersonic shock waves and high-speed weather patterns.

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