# Forces & Friction: Calculating Normal Force & Horizontal Force

• santoki
In summary, a man is pulling a 40.0 kg crate across a level floor with a horizontal force, and the coefficient of kinetic friction is μk = 0.59 for the crate and the floor. To find the normal force acting on the box, we can use the formula N = mg, which gives us a value of 392 N. To determine the horizontal force needed to accelerate the crate at 2.0 m/s2, we can use the equation N-Fx = max and solve for Fx, which gives us a value of 312 N. However, this does not take into account the frictional force, which is a vertical force and affects the acceleration of the crate. The relationship between the friction
santoki

## Homework Statement

A man is pulling a 40.0 kg crate across a level floor with a horizontal force, and the coefficient of kinetic friction is μk = 0.59 for the crate and the floor.

14. What is the normal force acting on the box?
a) 231 N
b) 340 N
c) 196 N
d) 392 N

15. What horizontal force must the man apply to get the crate to accelerate at 2.0 m/s2 ?
a) 311 N
b) 231 N
c) 81 N
d) 40 N

2. The attempt at a solution

For 14:
N = mg = (40.0)(9.8) = 392N

For 15:
N-Fx = max
392 - Fx = (40.0)(2.0)
Fx = 312N

but there's no 312N there and I didn't even incorporate the μk?

Did you draw a free body diagram? Is N a horizontal force or a vertical force?

Chet

Chestermiller said:
Did you draw a free body diagram? Is N a horizontal force or a vertical force?

Chet

N is a horizontal force.

santoki said:
N is a horizontal force.

No, it's a vertical force, the vertical component of the reaction from the floor.
What, then, is the frictional force?
What is the relationship between the frictional force, the applied force, and the resulting acceleration? (Your equation was wrong.)

Your calculations for the normal force and horizontal force appear to be correct. However, for question 15, you also need to take into account the frictional force, which is equal to μkN. So the equation should be N-Fx-μkN = max. Substituting the value for N, we get 392-Fx-(0.59)(392) = (40.0)(2.0). Solving for Fx gives a value of 234.8 N, which is closest to option a) 231 N. Therefore, the horizontal force the man must apply to get the crate to accelerate at 2.0 m/s2 is approximately 234.8 N.

## 1. What is normal force and how is it calculated?

The normal force is the force that a surface exerts on an object that is in contact with it. It is always perpendicular to the surface and is equal in magnitude to the force that the object applies on the surface. The normal force can be calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s²) and the cosine of the angle between the surface and the horizontal plane. This can be represented by the formula FN = mgcosθ.

## 2. What factors affect the normal force?

The normal force is affected by the mass and weight of the object, the angle of the surface, and the force of gravity. The normal force will increase if the object's mass or weight increases, or if the surface becomes more perpendicular to the horizontal plane. It will decrease if the surface becomes more parallel to the horizontal plane or if the force of gravity changes.

## 3. How is horizontal force calculated?

The horizontal force is the force that acts parallel to the surface. It can be calculated using the formula FH = μFN, where μ is the coefficient of friction and FN is the normal force. The coefficient of friction is a measure of the resistance between two surfaces and is dependent on the type of materials in contact and the force pushing the surfaces together.

## 4. Can the normal force be greater than the weight of an object?

Yes, the normal force can be greater than the weight of an object. This can happen if the object is on an incline or if there is an external force pushing down on the object. In these cases, the normal force will be equal to the sum of the weight of the object and the additional force.

## 5. How does friction affect the normal and horizontal forces?

Friction is a force that opposes motion between two surfaces in contact. It can affect both the normal and horizontal forces. Friction will increase the normal force and decrease the horizontal force, making it more difficult for an object to move. The amount of friction depends on the materials in contact and the force pushing the surfaces together.

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