Pulling a Box of Sand: Tension and Friction

[leroyjenkens]

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 792 N. The coefficient of static friction between the box and the floor is 0.37. (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

Maybe F=ma? I have no idea where to begin on this. So little information is given it makes me think there's some mistake.

The Attempt at a Solution

I drew a box with a string attached to it and that's all I could figure out. The book gives no examples that are even within a light year of being similar to this, so that thing is worthless.

 

[Spinnor]

You want to maximize m(θ) = C(sinθ + cosθ)

see,

 

[leroyjenkens]

You want to maximize m(θ) = C(sinθ + cosθ)

see,

Thanks for the response.

I still don't quite see how I can figure out the problem. I don't have enough numerical values to plug in, from what I can tell.

 

[Spinnor]

Plot sinθ + cosθ

You want to maximize m(θ) = C(sinθ + cosθ)

Set d m(θ)/dθ = 0

 

[asteriatic]

I can provide you with a proper response to this content. First of all, it is important to note that this problem is a classic example of a physics problem involving forces, specifically tension and friction. The given information is sufficient to solve the problem, and it is not necessary to assume any mistakes. Let's break down the problem and approach it step by step.

First, we need to understand the concept of tension. Tension is a pulling force that is transmitted through a flexible string, rope, or cable when it is pulled at both ends. In this case, the cable is used to pull the box of sand across the floor.

Next, we need to consider the coefficient of static friction. This is a measure of the amount of force required to overcome the friction between two surfaces in contact with each other. In this case, the box of sand and the floor are the two surfaces in contact.

Now, let's address the questions asked in the problem. The first question asks for the angle between the cable and the horizontal in order to pull the greatest possible amount of sand. This can be answered by understanding the concept of maximum static friction. This occurs when the applied force (in this case, the tension in the cable) is equal to the maximum possible friction force between the two surfaces. This can be represented by the equation: Fmax = μsN, where μs is the coefficient of static friction and N is the normal force between the two surfaces. In this case, the normal force is equal to the weight of the box and the sand, which brings us to the second question.

The weight of the sand and box can be calculated by using the equation: Fg = mg, where m is the mass of the box and sand, and g is the acceleration due to gravity (9.8 m/s^2). Since the problem does not provide the mass of the box and sand, we cannot calculate the weight. However, we can use the given information to find the angle that will maximize the amount of sand pulled.

We know that the tension in the cable should not exceed 792 N, and the coefficient of static friction is 0.37. Using the equation Fmax = μsN, we can rearrange it to find the normal force N. N = Fmax/μs = 792/0.37 = 2140.5 N. Now, we can use the concept of trigonometry to find