The Drum Shown in the Figure Has a Radius of $2.3 \mathrm { kq } \cdot \mathrm { m } ^ { 2 }$

question 74

Multiple Choice

The drum shown in the figure has a radius of 0.40 m and a moment of inertia of $2.3 \mathrm { kq } \cdot \mathrm { m } ^ { 2 }$ about an axis perpendicular to it through its center. The frictional torque at the drum axle is $3.0 \mathrm {~N} \cdot \mathrm { m }$ 14-m length of rope is wound around the rim. The drum is initially at rest. A constant force is applied to the free end of the rope until the rope is completely unwound and slips off. At that instant, the angular speed of the drum is 23 rad/s. The drum then slows down at a constant rate and comes to a halt. In this situation, what was the magnitude of the constant force applied to the rope?

• A) 51 N
• B) 40 N
• C) 18 N
• D) 29 N
• E) 7.5 N

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Definitions:

Marginal Cost

The amount of money needed to create an additional unit of a product or service.

Average Total Costs

The total costs of production (fixed and variable) divided by the quantity of output produced.

Total Fixed Costs

The sum of all costs that do not change with the level of production or services provided, such as rent and salaries.

Average Variable Cost

The total variable cost of producing a good divided by the quantity of the good produced, representing the variable cost per unit.