A package of mass m is placed inside a drum

In summary, to determine the static coefficient of friction between a package and a drum rotating at a constant angular speed, we can use the equation: μ = tan(θ) - (1/2)(ω^2/g). In this case, since the package reaches θ = 45° before slipping, the static coefficient of friction is μ = tan(45°) - (1/2)(1.36^2/9.8) = 0.414 - 0.009 = 0.405.
  • #1
Alexanddros81
177
4

Homework Statement


13.69 A packege of mass m is placed inside a drum that rotates in the vertical plane
at the constant angular speed ##\dot {θ} = 1.36 rad/s##. If the package reaches the position
θ = 45deg before slipping, determine the static coefficient of friction between the
package and the drum

Homework Equations

The Attempt at a Solution


Pytels_Dynamics084.jpg


Can you check my solution?
 
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  • #2
I like that you wrote your algebra in terms of a generic angle θ, but in doing so you opted for the wrong trig function somehwre. There should be a cosine in one place and a sine in the other. But since θ happens to be 45° this made no difference and you got the right answer.
 

1. What is the purpose of placing a package of mass m inside a drum?

The purpose of placing a package of mass m inside a drum is to protect the package and its contents. The drum provides a sturdy and enclosed environment that can shield the package from external factors such as impact, moisture, and temperature changes.

2. How does the mass of the package affect its placement in the drum?

The mass of the package is an important factor to consider when placing it inside a drum. The drum must be able to support the weight of the package without compromising its structural integrity. A package with a larger mass may require a stronger and more durable drum to ensure proper protection.

3. Can the placement of the package inside the drum affect its contents?

Yes, the placement of the package inside the drum can affect its contents. The package should be placed in a way that minimizes movement and shifting during transit. This can help prevent damage to the contents, especially if they are fragile.

4. Are there any safety precautions to consider when placing a package inside a drum?

Yes, there are some safety precautions to keep in mind when placing a package inside a drum. The package should be properly secured and cushioned to prevent it from shifting or falling out of the drum. It is also important to consider the weight distribution within the drum to avoid any balance issues during transportation.

5. Is there a limit to the size or weight of a package that can be placed inside a drum?

There may be limitations on the size or weight of a package that can be placed inside a drum, depending on the type of drum and its intended use. It is important to consult the manufacturer's guidelines or seek professional advice to ensure the package is suitable for the chosen drum.

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