# Help with force and friction on a flat surface

• Mattches
In summary, the problem involves a 30kg crate on a flat floor with a rope pulling it to the right with a force of 125N. The coefficients of static and kinetic friction are .34 and .24 respectively. The minimum force needed to stop the crate from moving is determined by using Newton's second law and equating the total static friction to the pulling force. The normal force, which is equal to the weight of the crate, must also be taken into account as it adds to the total friction. By relating static friction to the normal force, the minimum force needed to stop the crate can be calculated.
Mattches

## Homework Statement

I have a 30kg crate on a flat floor. There is a rope pulling the crate to the right with a force of 125N. The coefficients of static and kinetic friction are .34 and .24 respectively. I need to know what the minimum force I could put on top of the crate to stop it from moving.
Fg = 9.81 m/s^2
uS = .34
uK = .24
m = 30kg

## Homework Equations

I know that I need to use Newtons second law to determine the sum of all forces in each direction, and see how much needs to be added to overcome the 125N pull. But honestly I have no idea where to start!

## The Attempt at a Solution

I know that Fg on the crate is 294.3N. And I know that friction opposes the way the crate is being pulled. But I really don't know how to piece this problem together.
Can anyone help?

What must the total static friction be to keep the crate from moving? (Assuming it is initially at rest.)

How is max static friction related to the normal force between crate and floor?

The total static friction has to be equal to the force pulling the crate. The normal force is pushing the crate up at the same rate that gravity is pulling down but...I'm still not exactly sure where to go from there. Sorry but I'm very new at this :[

Mattches said:
The total static friction has to be equal to the force pulling the crate.
Good.
The normal force is pushing the crate up at the same rate that gravity is pulling down but...
That would be true if you didn't apply any additional force on the crate. But whatever force you push down on the crate with will add to the normal force.

How does static friction relate to the normal force? Use that fact (and your first statement in this post) to figure out what the total normal force needs to be for there to be enough friction.

As a scientist, it is important to approach problems in a systematic and logical manner. In this scenario, the first step would be to draw a free body diagram of the crate, showing all the forces acting on it. This will help in visualizing the problem and identifying the key components.

Given the mass of the crate (30kg), the force of gravity acting on it can be calculated using the formula Fg = mg, where m is the mass and g is the acceleration due to gravity (9.81 m/s^2). In this case, Fg = 294.3N.

Next, we need to consider the force of friction acting on the crate. Friction is a force that opposes motion, and it can be either static or kinetic depending on the situation. In this case, the crate is not moving initially, so we can assume that the force of friction is static. The formula for static friction is Fs = uS * N, where uS is the coefficient of static friction and N is the normal force (the force exerted by the surface on the object). In this scenario, N is equal to the force of gravity, so Fs = uS * Fg = 0.34 * 294.3 = 99.9N.

Since the crate is being pulled to the right with a force of 125N, we can determine the net force acting on the crate by subtracting the force of friction from the pulling force. Net force = 125N - 99.9N = 25.1N.

According to Newton's second law, the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is 25.1N and the mass is 30kg, so we can calculate the acceleration of the crate using the formula a = Fnet/m = 25.1N/30kg = 0.83 m/s^2.

Now, to determine the minimum force needed to stop the crate from moving, we need to consider the force required to counteract this acceleration. This force can be calculated using the formula F = ma, where m is the mass and a is the acceleration. In this scenario, F = 30kg * 0.83 m/s^2 = 24.9N.

Therefore, the minimum force that needs to be applied on top of the crate to stop it from moving is approximately 24.

## What is force?

Force is a push or pull that can cause an object to accelerate or change its motion. It is measured in units of Newtons (N) and is represented by an arrow pointing in the direction of the force.

## What is friction?

Friction is a force that opposes motion between two surfaces in contact. It is caused by the roughness of the surfaces and can be affected by factors such as the type of material, the force pushing the surfaces together, and the speed of the motion.

## How does force affect friction?

The greater the force pushing two surfaces together, the greater the friction between them. This means that a heavier object will experience more friction than a lighter one. Additionally, the direction of the force can also impact the amount of friction.

## How can friction be reduced?

There are a few ways to reduce friction on a flat surface. One way is to use lubricants, such as oil or grease, to create a slippery layer between the surfaces. Another method is to use smoother materials for the surfaces, which will have less resistance and result in less friction.

## What is the difference between static and kinetic friction?

Static friction is the force that prevents two stationary surfaces from moving against each other. Kinetic friction, on the other hand, is the force that opposes the motion of two surfaces that are already in motion. Static friction is typically greater than kinetic friction.

Replies
6
Views
2K
Replies
6
Views
2K
Replies
6
Views
384
Replies
6
Views
8K
Replies
4
Views
3K
Replies
6
Views
2K
Replies
6
Views
5K
Replies
10
Views
2K
Replies
7
Views
3K
Replies
4
Views
5K