# How to Solve a Basic Sliding Box Problem on a Frictionless Ramp?

• Brendan Webb
In summary, the problem involves a 90 kg box being pushed up a ramp at a constant speed by a horizontal force, with the ramp being inclined at 28° and assumed to be frictionless. Using a right angle calculator, a horizontal force of 468 N is determined to be sufficient to counteract the force of gravity pulling the box down the ramp. The normal force on the box is not relevant for solving this problem.
Brendan Webb
HW Template missing as it was moved from another forum
Hi

A 90 kg box is pushed by a horizontal force F at constant speed up a ramp inclined at 28°, as shown. Determine the magnitude of the applied force.
1. when the ramp is frictionless.

My attempt at a solution.

I diagrammed the problem as in the file uploaded. To figure out the horizontal force required to counter the force of the box sliding down the incline I figured that the horizontal force would have to be the hypotenuse because it needs to be stronger than both Fn and Fg(sin28). However, it shows the normal force being larger than Fg(sin28) in terms of side lengths when it should be the opposite way around. I am confused on how to solve this problem even though it has been posted before on this website. Any help would be much appreciated.

Thanks
Brendan

#### Attachments

• Physics Diagram.jpg
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Using a right angle calculator I came up with a more logical answer of 468 N. But that leaves the opposite side of my triangle at 220 N which I am not sure how I would get. Or would that 220 N be the Normal force pushing back against my horizontal force? If it is then I guess in this question it is inconsequential to know the normal force of the box against the ramp.

Brendan Webb said:
I guess in this question it is inconsequential to know the normal force of the box against the ramp.

Indeed. The component of F directed up the incline just needs to be equal and opposite to the force of gravity directed down the incline.
I got pretty much the same answer as you. Now, if they had asked for the normal force on the box...

Brendan Webb
Thanks for the verification!

## 1. What is the Basic Sliding Box Problem?

The Basic Sliding Box Problem is a mathematical puzzle that involves a rectangular box with dimensions that can slide into another rectangular box with different dimensions. The goal is to determine the maximum number of times the smaller box can fit into the larger box without any overlapping or gaps.

## 2. What are the key components of the Basic Sliding Box Problem?

The key components of the Basic Sliding Box Problem include the dimensions of the two rectangular boxes, the dimensions of the smaller box, and the dimensions of the larger box. These components are needed to calculate the maximum number of times the smaller box can fit into the larger box.

## 3. How is the solution to the Basic Sliding Box Problem calculated?

The solution to the Basic Sliding Box Problem is calculated by dividing the dimensions of the larger box by the dimensions of the smaller box. This will give the maximum number of times the smaller box can fit into the larger box without any overlapping or gaps.

## 4. Are there any real-life applications for the Basic Sliding Box Problem?

Yes, the Basic Sliding Box Problem is commonly used in packaging and logistics industries to determine the most efficient way to pack items into boxes and containers. It is also used in computer science and programming to optimize algorithms and data structures.

## 5. Are there any variations of the Basic Sliding Box Problem?

Yes, there are variations of the Basic Sliding Box Problem that involve different shaped boxes or boxes with varying dimensions. There are also more complex versions that involve multiple boxes and different constraints. These variations are used to test problem-solving skills and critical thinking abilities.

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