Terminal Velocity of Cube: 1.6 m/s

In summary, the terminal velocity of a cube with a drag coefficient of 0.90 and a side length of 1.0 cm in air with a density of 1.2 kg/m^3 is 17.04 m/s, but the given answer of 1.6 m/s may be incorrect.
  • #1
Dalip Saini
16
0

Homework Statement


cube has a drag coefficient of 0.90. What would the terminal velocity of this cube be, 1.0 cm on a side in air (ρ = 1.2 kg/m3)? Take the density of this cube to be 1.6 x 103 kg/m3.


  • A

    68 m/s


  • B

    1.6 m/s


  • C

    5.6 m/s


  • D

    20 m/s


  • E

    360 m/s
Correct answer is 1.6 m/s

Homework Equations


terminal speed = sqrt[(2mg)/(Cpa)]
volume*density = mass

The Attempt at a Solution


(0.01 m)^3(1.6E3 kg/m^3) = 1.6E-3 kg
terminal speed = sqrt [((2(1.6E-3)(9.8))/((0.9)(1.2)(0.01)^2)] = 17.04 m/s but the answer is 1.6 m/s. I don't understand what I did wrong.
 
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  • #2
Lots of numbers to chase, but 1.6 m/s makes no sense.
 
  • #3
Hint: the given answer isn't always right!
(I got same as yours).
 

1. What is the terminal velocity of a cube?

The terminal velocity of a cube is 1.6 m/s. This means that when the cube is falling through a liquid or gas, its speed will eventually reach a constant value of 1.6 m/s due to the balancing forces of gravity and air resistance.

2. How is the terminal velocity of a cube calculated?

The terminal velocity of a cube is calculated using the formula v = √(2mg/ρAC), where v is the terminal velocity, m is the mass of the cube, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the cube, and C is the drag coefficient.

3. What factors affect the terminal velocity of a cube?

The terminal velocity of a cube is affected by the cube's mass, size, shape, and the properties of the fluid it is falling through. Other factors such as air temperature and pressure can also have an impact.

4. Can the terminal velocity of a cube change?

Yes, the terminal velocity of a cube can change depending on the conditions it is falling through. For example, if the cube is falling through a denser fluid, its terminal velocity will be higher. Changes in the cube's shape or size can also affect its terminal velocity.

5. Why is the terminal velocity of a cube important to study?

Understanding the terminal velocity of a cube is important for a variety of applications, such as designing parachutes, calculating the impact force of falling objects, and studying fluid dynamics. It can also provide insight into the behavior of objects in different environments and help us make predictions about their motion.

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