# How Do You Calculate Force on an Inclined Plane with and without Friction?

• questionable
In summary: The component parallel to the incline will help you understand the answer to part (a).In summary, to solve this problem you need to break down the force of gravity into components parallel and perpendicular to the ramp. For part (a), the force of gravity does not contribute to the box's motion, so you can ignore the perpendicular component. The parallel component of the force of gravity is equal to the applied force, F, which is needed to keep the box moving up the ramp at a constant speed. For part (b), the force of friction, which is equal to μk * Fn, must be added to the parallel component of the force of gravity to find the magnitude of the applied force needed to keep the box moving up
questionable

## Homework Statement

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:
a. when the ramp is frictionless.
b. when the coefficient of kinetic friction is 0.18.

## Homework Equations

F= ma, Ffr = μk * Fn

## The Attempt at a Solution

Everywhere I look online I keep getting told that for part (a) I need to do sin28 * 882N (i.e. sin28 * mg) but I have NO idea why. Could somebody draw me a picture of the vector decomposition because I really really do not understand why you'd multiply.

For part (b) my course hasn't even taught us about kinetic friction yet, but through looking around I've found out that Ffr = μk * Fn. So once I've found the force of friction, what do I do with it?

Thanks for any help...

questionable said:

## Homework Statement

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:
a. when the ramp is frictionless.
b. when the coefficient of kinetic friction is 0.18.

## Homework Equations

F= ma, Ffr = μk * Fn

## The Attempt at a Solution

Everywhere I look online I keep getting told that for part (a) I need to do sin28 * 882N (i.e. sin28 * mg) but I have NO idea why. Could somebody draw me a picture of the vector decomposition because I really really do not understand why you'd multiply.

For part (b) my course hasn't even taught us about kinetic friction yet, but through looking around I've found out that Ffr = μk * Fn. So once I've found the force of friction, what do I do with it?

Thanks for any help...

Have you tried drawing a diagram?

If you upload a picture of your attempt I can see where you're having the issue.

The key to these questions are good force diagrams, so having one drawn for you won't solve anything in the long run.

BOAS said:
Have you tried drawing a diagram?

If you upload a picture of your attempt I can see where you're having the issue.

The key to these questions are good force diagrams, so having one drawn for you won't solve anything in the long run.

This is the closest guess that I have. I don't have a clue really. Sorry for the bad drawing.

#### Attachments

• Untitled-1.png
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questionable said:
This is the closest guess that I have. I don't have a clue really. Sorry for the bad drawing.

Just focus on the force of gravity for a moment. Draw it so that the force of gravity is the hypotenuse and the two legs are parallel and perpendicular to the ramp. (This way you've broken up the force of gravity into the components perpendicular to the ramp and parallel to the ramp.)

Then just think about the frictionless case. If the box is kept at a constant velocity, then what must be true? How can you make this true?

Okay, I've done that. What are the components of the gravity vector though? Isn't it just pointing down?

questionable said:
Okay, I've done that. What are the components of the gravity vector though? Isn't it just pointing down?

The weight of the box does point straight down, but think about the direction of the normal force, and you should see that you need to decompose mg into two components.

questionable said:
Okay, I've done that. What are the components of the gravity vector though? Isn't it just pointing down?
Yes, but the coordinate system imposed in the solution is one in which the axes are parallel and perpendicular to the plane of the incline. In this case, you can decompose the gravity vector along these mutually orthogonal directions.

## What are Newton's three laws of motion?

Newton's first law states that an object at rest will stay at rest and an object in motion will stay in motion with a constant velocity unless acted upon by an unbalanced force. Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Newton's third law states that for every action, there is an equal and opposite reaction.

## What is the difference between mass and weight?

Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. Mass is constant and does not change with location, while weight can vary depending on the strength of gravity.

## What is the role of forces in Newton's laws?

Forces are essential in understanding Newton's laws as they are the cause of changes in motion. According to Newton's first law, an object will remain at rest or in motion unless acted upon by an unbalanced force. Newton's second law explains how forces affect an object's acceleration, and Newton's third law explains how forces always act in pairs.

## How do forces affect the motion of an object?

Forces can cause an object to change its speed or direction of motion. A force acting in the same direction as an object's motion will cause it to speed up, while a force acting in the opposite direction will cause it to slow down. Additionally, a force acting perpendicular to an object's motion can cause it to change direction.

## How do Newton's laws apply to everyday life?

Newton's laws of motion can be observed in everyday life in various situations. For example, the first law explains why objects stay at rest unless a force is applied, such as a ball remaining still until someone kicks it. The second law can be seen in the acceleration of a car when the gas pedal is pressed, and the third law can be observed when a person jumps off a diving board and feels a force pushing them up as they push off the board.

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