# Newton's 2nd law problem. I have trouble setting up eq. for gravity/weight

• Sentience
In summary, the conversation discusses setting up equations for forces acting on a block on an incline, with a given initial velocity, angle, and coefficient of kinetic friction. The person is struggling with handling positive and negative signs and the instructor recommends drawing a free body diagram and setting up a coordinate system to make the situation less confusing. They also provide a sample free body diagram for reference.
Sentience

## Homework Statement

A block is given a push up the incline so it has an initial velocity of 5 m/s up the incline. If the incline angle is 30 degrees and the coefficient of kinetic friction is 0.2, what will be the stopping distance of the block?

## Homework Equations

F = m * a

Force of friction = mu * Fn

## The Attempt at a Solution

I do just fine until I go to set up the equation for the forces acting in the x direction. When this block is pushed it will move up the incline a bit, then come back down the incline because of friction and gravity. Both of these forces are pointing down in the incline right?

If you click on the solution, my instructor has it set up so both forces are negative. It just seems like going to the right would be the positive x direction.

Could I instead write it out so both are positive?

I feel like I understand everything in these problems just fine, I just set get the sign on one of my components wrong. (usually gravity acting in the horizontal direction) Do you have a foolproof way of setting them up consistently so your signs aren't off?

Last edited by a moderator:
You are struggling with a very common problem. Handling positive and negative signs requires a free body diagram (picture of forces), coordinate system, and experience.

First, you could set up a coordinate system where gravity and friction are positive, but I don't recommend it because the situation becomes more confusing. You should understand that a coordinate system can be pointed in any direction. The x-axis doesn't always point to the right. The person solving the problem decides the most convienent orientation for the coordinate system.

Here is what I would do:
1.) Draw the object with all the forces acting on it. Do not include the anything else (such as the ramp) because the picture just gets more complicated.
2.) Draw the coordinate system with the positive x-axis pointing in the direction that the object is moving and the positive y-axis pointing perpendicular to the surface. Do not assume that the x-axis always has to be to the right and the y-axis has to be vertical.
3.) Break all forces into x and y components. (Respond if you aren't familiar with components. I'll describe them in detail.)
4.) Set up an x force equation by adding all x component forces together. Write them as positive if they are pointing in the positive x direction and negative if they are pointing in the negative y direction.
5.) Repeat Step (4.) for the y force equation.

I attached a sample free body diagram for you to see what I'm talking about.

Let me know if this seems too confusing. I can try and simplify it for you. I'm not sure what your current understanding is.

#### Attachments

• Force Body Diagram.png
9.8 KB · Views: 453

## 1. What is Newton's 2nd law and how does it relate to gravity?

Newton's 2nd law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the greater the force on an object, the greater its acceleration will be, and the more massive an object is, the less it will accelerate. Gravity is a force that acts on all objects with mass, and it follows the principles of Newton's 2nd law.

## 2. How do I set up equations for gravity and weight in Newton's 2nd law problems?

To set up equations for gravity and weight in Newton's 2nd law problems, you first need to identify all the forces acting on the object. In the case of gravity, the force acting on an object is its weight, which is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2 on Earth). Once you have identified the forces, you can use Newton's 2nd law to set up equations and solve for the desired variables.

## 3. What is the formula for weight and how is it related to mass and gravity?

The formula for weight is W = mg, where W is weight, m is mass, and g is the acceleration due to gravity. This formula shows that weight is directly proportional to mass and the acceleration due to gravity. This means that as an object's mass or the acceleration due to gravity increases, its weight will also increase.

## 4. What units should I use when working with Newton's 2nd law problems involving gravity?

In Newton's 2nd law problems, it is important to use consistent units for all measurements. The most commonly used units for mass are kilograms (kg) and for force are Newtons (N). However, when working with gravity, it is also common to use units of weight, such as pounds (lb) or Newtons (N). Just be sure to convert all units to the same system before setting up and solving equations.

## 5. How does the angle of an object affect the force of gravity in Newton's 2nd law problems?

The angle of an object does not affect the force of gravity in Newton's 2nd law problems. Gravity is a downward force that acts on all objects regardless of their orientation or angle. However, the angle of an object may affect the components of the forces acting on it, which would need to be taken into account when setting up equations for Newton's 2nd law.

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