Maximizing Sand Pulled: Angle & Weight

In summary, the task is to determine the maximum amount of sand that can be pulled across a floor without exceeding a tension of 1220N in the cable. The coefficient of static friction between the box and the floor is given as 0.24. To calculate this, a free body diagram can be used to identify the forces acting on the box. The weight of the sand and box can then be determined using Newton's First Law in the y direction and Newton's First Law in the x direction at the limit of the static friction force.
  • #1
coffeebird
15
0

Homework Statement



An initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 1220N. The coefficient of static friction between the box and the floor is 0.24. (a)What should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand, and (b) what is the weight of the sand and box in that situation?


Homework Equations





The Attempt at a Solution



dm/dθ= (-F/a)cosθ...
 
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  • #2
Before the object can accelerate, it first has to overcome static friction in the equilibrium condition(a =0). m is maximized when dm/dθ = ?. Try a free body diagram to identify forces acting, and use Newton 1 in the y direction , and Newton 1 in the x direction at the limiting value of the static friction force.
 

FAQ: Maximizing Sand Pulled: Angle & Weight

What is the purpose of maximizing sand pulled?

The purpose of maximizing sand pulled is to increase the efficiency and effectiveness of sand dredging operations. By finding the optimal angle and weight for pulling sand, a greater amount of sand can be extracted in a shorter amount of time.

How does the angle affect the amount of sand pulled?

The angle at which the dredge is pulled affects the amount of sand pulled by determining the area that is covered by the dredge. A steeper angle will cover a smaller area, resulting in less sand being pulled, while a shallower angle will cover a larger area, resulting in more sand being pulled.

What is the role of weight in maximizing sand pulled?

The weight of the dredge is a key factor in maximizing sand pulled. A heavier dredge will sink deeper into the sand, allowing for more sand to be extracted. However, if the weight is too heavy, it may become difficult to pull the dredge through the sand.

Is there an optimal angle and weight for maximizing sand pulled?

Yes, there is an optimal angle and weight for maximizing sand pulled. This can vary depending on factors such as the type of sand, water conditions, and the power of the dredge. It is important to conduct experiments and gather data to determine the most effective angle and weight for a specific dredging operation.

What are some potential challenges in maximizing sand pulled?

Some potential challenges in maximizing sand pulled include unfavorable water and weather conditions, equipment malfunctions, and limitations in resources and funding. It is important to carefully plan and strategize to overcome these challenges and optimize sand dredging operations.

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