A horizontal force of 100 N is required to push a box across the floor at a constant velocity.

a) Show that the net force acting on the box is zero.

b) Show that the friction force that acts on the box is 100 N.

a. Fap-Ff = m*a = m*0

Fap - Ff = 0
The velocity is constant. Therefore,
the acceleration is zero.
Fap = Force applied.
Ff = Force of friction.

b. Fap - Ff = 0
100 - Ff = 0
Ff = 100 N.

a) Well, if the box is moving at a constant velocity, that means there's no acceleration. And according to Newton's second law, F = ma, if there's no acceleration, then there must be no net force acting on the box. So, in this case, the net force acting on the box is indeed zero.

b) Now, let's talk about the friction force. Since the box is moving at a constant velocity, that means there's no acceleration. And if we assume there's no other forces acting on the box, except the applied force of 100 N, and the friction force, we can conclude that the friction force must be equal in magnitude, but opposite in direction to the applied force. So, in this case, the friction force acting on the box is also 100 N.

And remember, friction can be a slippery subject sometimes, but I'll try my best to keep things running smoothly!

a) To show that the net force acting on the box is zero, we need to consider Newton's first law of motion, which states that an object at rest or moving at a constant velocity will continue to do so unless acted upon by an external force.

Since the box is moving at a constant velocity, we know that the acceleration is zero. According to Newton's second law of motion, the net force acting on an object is equal to the product of its mass and acceleration.

Since the acceleration is zero, the net force must also be zero. In this case, the horizontal force of 100 N is balanced by an equal and opposite force, resulting in a net force of zero.

b) To show that the friction force acting on the box is 100 N, we need to consider the relationship between the applied force and the friction force.

The applied force is 100 N, and since the box is moving at a constant velocity, the net force is zero. This means that the friction force must also be 100 N in the opposite direction.

Friction is often modeled as a force that opposes motion. In this case, the friction force acts in the opposite direction of the applied force to balance it out and allow the box to move at a constant velocity. So, the friction force acting on the box is 100 N.

a) To show that the net force acting on the box is zero, we can start by using Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma). However, since the box is moving at a constant velocity, it means that its acceleration is zero. Therefore, the net force acting on the box must also be zero.

b) Now, to show that the friction force that acts on the box is 100 N, we need to understand that in this situation, the force of 100 N that is being applied to the box is exactly equal to the friction force opposing its motion. This means that the applied force and the friction force are in equilibrium.

Friction force can be calculated using the equation Ff = μFn, where Ff is the friction force, μ is the coefficient of friction, and Fn is the normal force. In this case, since the box is on a horizontal surface, the normal force is equal to the weight of the box (mg), where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).

So, we have Ff = μmg. However, in this case, the box is moving at a constant velocity, so the friction force must be equal to the applied force, which is 100 N. Therefore, we can write:

Ff = 100 N = μmg

Since we want to find the value of the friction force, we can rearrange the equation to solve for Ff:

Ff = 100 N = μmg

Divide both sides of the equation by μ:

Ff/μ = mg

Finally, substitute the known values: μ = Ff/100 N, m = mass of the box, and g = 9.8 m/s^2.

So, when you have the values for mass and the coefficient of friction, you can substitute them into the equation to calculate the friction force. In this case, the friction force is equal to 100 N, as given in the problem statement.