How Do You Solve an Inclined Plane Problem Involving Friction and Force?

[livvy07]

Homework Statement

A box is pulled up an incline which is 285 m long and in the process the box rises 16.7 m. The force pulling the truck is 18300 N.
A) If there was no friction, what is the weight and mass of the box? B)If friction provides a force of 17,400 N, what is the force pulling the box?
c) What is the IMA?

The Attempt at a Solution

A)The weight would just be 18300 N I believe, since it is the effort force. and w=mg, so 18300=m(9.81), so m=1865.4 g?
B) 18300-17400=900 N force pulling box
C) IMA=De/Dr To find the effort distance,would you square 16.7+square 285?
=81504/16.7
=4880m
Im really confused on inclined planes, so any tips on what I am doing wrong would be great :)

 

[LowlyPion]

There is no statement that it was constant velocity, but I think over this distance it can be assumed. That means that the force is not lifting the weight the whole way, but rather is pulling it up the incline at an angle to gravity given in the problem by the rise of 16.7 m divided by the 285 m.

If you add friction, why is it you aren't adding that to the 18,300?

And can you explain what you are calling IMA?

 

[nlightner]

I would like to clarify and provide a more thorough explanation for the inclined plane problem.

Firstly, it is important to understand the concept of inclined planes. An inclined plane is a simple machine that is a flat surface that is raised at an angle. It allows us to reduce the amount of force needed to move an object to a higher elevation by increasing the distance over which the force is applied.

Now, let's address the homework statements one by one:

A) If there was no friction, what is the weight and mass of the box?

Without friction, the only force acting on the box is the force pulling it up the incline, which is 18300 N. This force is also known as the effort force. The weight of an object is defined as the force of gravity acting on it, which is equal to its mass multiplied by the acceleration due to gravity (9.81 m/s^2). Therefore, the weight of the box would be 18300 N. To find the mass, we can use the formula w=mg, where w is the weight, m is the mass, and g is the acceleration due to gravity. Rearranging the formula, we get m=w/g, so the mass of the box would be 1865.4 kg.

B) If friction provides a force of 17,400 N, what is the force pulling the box?

In this case, we have to take into account the frictional force acting on the box, which is 17,400 N. This force is acting in the opposite direction of the force pulling the box up the incline. Therefore, the net force pulling the box would be 18300 N - 17400 N = 900 N.

C) What is the IMA?

IMA stands for Ideal Mechanical Advantage, which is a measure of the effectiveness of a machine in reducing the effort force needed to perform a task. In this case, the inclined plane is the simple machine, and the effort force is the force pulling the box up the incline. The IMA of an inclined plane is given by the formula IMA = De/Dr, where De is the effort distance (the distance over which the effort force is applied) and Dr is the resistance distance (the distance over which the weight of the object is lifted). In this problem, De is 285 m (length of the incline) and Dr is 16.7 m (height