# How do you find the normal force of an object being pushed?

• Maya KDeoimmich
In summary, the problem involves a 42 kg wagon being pushed with a force of 449 N at an angle of 46 degrees with the horizontal. The forces acting on the wagon are gravity, friction, applied force, and normal force. To find the normal force and acceleration, you will use Newton's laws and set up two equations for vertical and horizontal forces. The sum of vertical forces must equal the weight of the wagon and the coefficient of kinetic friction should be taken into account.
Maya KDeoimmich

## Homework Statement

A 42 kg wagon is being pushed with a metal rod that makes an angle of 46 with the horizontal. The applied force is 449 N and the coefficient of kinetic friction between the wagon and the ground is 0.21.
I'm not sure what equation to use to find the normal force and then the acceleration. Thanks!

Fy = mgcos46-N

## The Attempt at a Solution

Last edited:
Maya KDeoimmich said:
I'm not sure what equation to use to find the normal force and then the acceleration.
You'll use Newton's laws, of course.

First step: What forces act on the wagon? (I count three forces.)

Ok thanks but can you please walk me through the steps of how to find the normal force and the acceleration

First answer my question. What forces act on the wagon?

Gravity, friction, and the applied force

Maya KDeoimmich said:
Gravity, friction, and the applied force
Oops, one more force acts. (I meant to say four, not three.) But those three are good. What's missing?

normal force? not sure

Maya KDeoimmich said:
normal force? not sure
Exactly.

Now you'll set up two equations: One for vertical forces (vertical components) and another for horizontal forces.

Hint: What must the sum of the vertical forces equal?

Maya KDeoimmich said:
an angle of 46 with the horizontal
Which way? I.e. is it tending to push down on the wagon or up on it?
Maya KDeoimmich said:
Fy = mgcos46-N
How do you get that? Isn't the mg vertical?
Maya KDeoimmich said:
the coefficient of kinetic friction between the wagon and the ground is 0.21
Ouch! Unless the wheels are locked they mean rolling resistance, not friction, but don't worry about that for now.

## 1. How do you calculate the normal force of an object?

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 object and the surface it is resting on. This formula can be written as N = mgcosθ, where N is the normal force, m is the mass of the object, g is the acceleration due to gravity, and θ is the angle between the object and the surface.

## 2. What is the difference between weight and normal force?

Weight is the force exerted on an object by gravity, while normal force is the force exerted by a surface on an object in contact with it to prevent the object from falling through the surface. Weight is a vector quantity, while normal force is a scalar quantity. Additionally, weight always acts downwards, while normal force can act in any direction perpendicular to the surface.

## 3. Can the normal force be negative?

No, the normal force cannot be negative. It always acts perpendicular to the surface and in the opposite direction of any external force applied to the object. Therefore, the normal force will always have a positive value.

## 4. How does the normal force change when an object is pushed at an angle?

When an object is pushed at an angle, the normal force will change depending on the angle between the object and the surface. The normal force will decrease as the angle increases, and it will become zero when the object is pushed parallel to the surface.

## 5. Is the normal force always equal to the weight of an object?

No, the normal force is not always equal to the weight of an object. The normal force is only equal to the weight when the object is at rest and there are no other forces acting on it. In other cases, such as when the object is accelerating or being pushed at an angle, the normal force will be different from the weight.

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