Newton's third law says that for every force, there is an equal and opposite force: for an object on a non-inclined plane, the force of gravity is straight down and the normal force is straight up.

(For non-inclined planes,  still works, just use  for your  as the cosine of  is .)

In non-mathematical terms, the normal force is what keeps us from sinking into the ground: we experience the force of gravity and yet we aren't sucked into the Earth's crust. Why? Because the object we stand upon provides an equal but opposite force on our feet.

This principle still applies to objects on an inclined plane. As the angle of the plane increases, the force of gravity is divided. Gravity causes the object to travel downward and horizontally along the plane's surface. The normal force must still counteract the downward portion of gravity, but will be less than the total gravitational force since the object is sliding horizontally. This requires us to use the cosine term to reduce the total normal force. Eventually, if the angle of incline increases enough, we would be taking , which is zero; if the object is in free fall (the plane is vertical), then there is no normal force.

The normal force on an object at rest on a flat surface is equal to the gravitational force on that object. In equation form, that means .

Use Newton's second law () to solve for the gravitational force, using acceleration due to gravity as your .

As normal force is the opposite of the gravitational force, we can see that .

Looking at our given values, we can see that each term only has one significant figure, since zeroes in front of the decimal are not significant. We can immediately determine that our answer will also have one significant figure however, to maintain accuracy, we will only round for precision after the final calculation.

The normal force acting on box is equal and opposite to the weight of the box. When the box is on a level surface, this term is equal to the force of gravity.

Use our given mass and the acceleration due to gravity to solve for the normal force of the box.

This value is equal to the total upward force on the box to counter its weight. When the man is lifting the box, he accommodates part of this upward force, lessening the normal force.

Find the final normal force by subtracting the force from the man from the total upward force.

Our given numbers only allow for one significant figure, so we must round down.

Normal force is defined as the force that a surface exerts on an object. If the object is at rest, net force on the object is equal to zero; therefore, the downward force (weight) must be equal to the upward force (normal force).

Since weight acts in the downward direction it will be negative. The total sum of the forces must be zero, in order for the object to be at rest.

This is also in accordance with Newton's third law, which suggests that the normal force will be equal and opposite the force of weight.

Normal force is the force that the table pushes onto the block. If the force on the block from gravity is pushing the block downward, then the normal force has to push straight upward to keep the block at rest. Since the block is not moving, these two forces must be equal and opposite to produce a net force of zero.

Since normal force is pushing upward, it will be positive. (The force of gravity would be negative).

The correct answer is 43N. Since the box is on an incline, normal force balances with the component of gravity that is perpendicular to the surface of the incline.

Note that the normal force is in the upward (positive) direction, while gravitational acceleration and the force of gravity are in the downward (negative) direction.

We are given the weight of the box (note that it will be downward and, therefore, negative):

Use this to solve for the normal force.

Normal force always acts perpendicular to the contact surface. It can act counter to gravity or to any other force that pushes an object against a surface.

Think of normal force as the force that keeps a surface solid; without normal force, an object would pass right through a surface. With this in mind, consider a book that you push against a wall in the horizontal direction such that it is in equilibrium and does not slide down the wall. In this case, normal force is acting counter to your pushing force along the horizontal axis and perpendicular to the force of gravity. Another example is any object placed on an inclined plane; in this system the normal force will act perpendicular to the incline and will only counter a portion of the gravitational force.

The equation for the force of friction is , where  is the coefficient of static friction.

The normal force is equal to the mass times acceleration due to gravity, but in the opposite direction (negative of the force of gravity).

Since the problem tells us that the force due to friction is , we can plug these values into our original equation to solve for the coefficient of friction.

The coefficient of friction has no units.

The equation for the force of friction is , where  is the coefficient of static friction.

The normal force is equal to the mass times acceleration due to gravity, but in the opposite direction (negative the force of gravity).

Since the problem tells us that the coefficient due to friction is equal to , we can plug these values into our original equation to solve for the force.

As the force due to friction is moving in the OPPOSITE direction to the force Mary will exert, it should appropriately be labelled as negative.

The equation for the force due to friction is , where  is the coefficient of kinetic friction. Since there is only one force acting upon the object, the force due to friction, we can find its value using the equation . We can equate these two force equations, meaning that . We can solve for the normal force, but we need to find  in order to find .

The problem gives us the mass of the crate, but we have to solve for the acceleration.

Start by finding the initial velocity. The problem gives us distance, final velocity, and change in time. We can use these values in the equation below to solve for the initial velocity.

Plug in our given values and solve.

We can use a linear motion equation to solve for the acceleration, using the velocity we just found. We now have the distance, time, and initial velocity.

Plug in the given values to solve for acceleration.

Now that we have the acceleration and the mass, we can return to our first equation for force.

The normal force is the same as the mass times gravity.

In this format, the masses cancel on both sides of the equation/

Now we can plug in our value for acceleration and gravity to solve for the coefficient of friction.