Finding the average magnitude of the drag force

In summary: Here, the force is not constant, but is a function of speed. You will need to use calculus to find the average force.In summary, a saucer with a mass of 1.75x10^9 enters the atmosphere of PlanetX, which has a uniform gravitational field of 10.6 m/s2. The saucer enters at a speed of 460 m/s and slows down to 110 m/s before crashing. The goal is to find the average magnitude of the drag force, taking into account the fact that gravity cannot be ignored. Using the equation for drag force on a disk and the concept of mechanical energy, an attempt was made to find the average force. However, this method is not valid
  • #1
rickyjoepr
6
1

Homework Statement



A saucer of mass 1.75x10^9 enters
1.the gravitational field of PlanetX and enters its atmosphere; the gravitational field of the planet is 10.6 m/s2 and is considered uniform throughout the 80-km thick atmosphere.
If the saucer enters the atmosphere at 460 m/s and slows down to 110 m/s before its crash-landing, what is the average magnitude of the drag force (gravity cannot be neglected)?
[/B]

Homework Equations



drag for disk, D = (1/4) AV^2
W = Total Mechanical Energy

The Attempt at a Solution



E1 = (1/2)m1Vi^2 + mgd
E2 = 0 + 0

So W = (1/2)m1V1+mgd

Because W = Fd

W/d = F

2.55 x10^10

However the correct answer is listed as 2.07 x 10^10 N

I am not sure if my method of using mechanical energy is correct., Or wether I should be using the drag force equation to solve the problem
 
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  • #2
rickyjoepr said:

Homework Statement



A saucer of mass 1.75x10^9 enters
1.the gravitational field of PlanetX and enters its atmosphere; the gravitational field of the planet is 10.6 m/s2 and is considered uniform throughout the 80-km thick atmosphere.
If the saucer enters the atmosphere at 460 m/s and slows down to 110 m/s before its crash-landing, what is the average magnitude of the drag force (gravity cannot be neglected)?
[/B]

Homework Equations



drag for disk, D = (1/4) AV^2
W = Total Mechanical Energy

The Attempt at a Solution



E1 = (1/2)m1Vi^2 + mgd
E2 = 0 + 0

So W = (1/2)m1V1+mgd

Because W = Fd

W/d = F

2.55 x10^10

However the correct answer is listed as 2.07 x 10^10 N

I am not sure if my method of using mechanical energy is correct., Or wether I should be using the drag force equation to solve the problem
The speed is not zero before the crash.
 
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  • #3
rickyjoepr said:
W/d = F
The use of this to find an average force is not valid, though I realize it is what you are forced to use in this question.
Average force is defined as (change in momentum)/(elapsed time). If the force is not constant then (change in energy)/(distance) will not usually produce the same value.
 
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Related to Finding the average magnitude of the drag force

1. What is the definition of drag force?

The drag force is a resistance force that acts opposite to the direction of motion of an object as it moves through a fluid (such as air or water). It is caused by the interaction between the object and the fluid molecules.

2. How is drag force calculated?

The drag force can be calculated using the equation Fd = 1/2 * ρ * v^2 * Cd * A, where ρ is the density of the fluid, v is the velocity of the object, Cd is the drag coefficient, and A is the cross-sectional area of the object.

3. What is the average magnitude of the drag force?

The average magnitude of the drag force is the average value of the drag force over a given time period or distance. It is calculated by taking the integral of the drag force equation over the specified time or distance and dividing it by the total time or distance.

4. How does air resistance affect the average magnitude of the drag force?

Air resistance, or the force of air pushing against the object as it moves through the air, is a type of drag force. Therefore, it will increase the average magnitude of the drag force as it adds to the overall resistance of the object's motion.

5. Can the average magnitude of the drag force be reduced?

Yes, the average magnitude of the drag force can be reduced by changing the shape of the object to decrease its cross-sectional area, increasing the fluid's viscosity, or decreasing the velocity of the object. Additionally, using aerodynamic designs and smooth surfaces can also help reduce the drag force.

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