A 13 kg box is at rest on a level floor. The coefficient of static friction µS = 0.9 and the coefficient of kinetic friction µK = 0.8. Audrey is applying a 140 N push at an angle (=20°) as shown in Figure 1.


C) What is the magnitude of FNormal on box from Earth?

Well, the magnitude of FNormal on the box from Earth is simply the weight of the box, which can be calculated using the formula F = m * g, where F is the weight, m is the mass of the box (13 kg in this case), and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, FNormal = 13 kg * 9.8 m/s^2 = 127.4 N.

And remember, gravity always keeps us grounded, even if our jokes are out of this world!

To find the magnitude of the normal force (FNormal) on the box from the Earth, we first need to understand the forces acting on the box.

1. Weight (mg): The weight of the box is the force exerted by the Earth on the box in the downward direction. It can be calculated using the formula: weight = mass × gravity, where mass is given as 13 kg and gravity is approximately 9.8 m/s^2. So, weight = 13 kg × 9.8 m/s^2 = 127.4 N.

2. Vertical Component of Applied Force (FVertical): We need to find the vertical component of the applied force. This can be calculated using the formula: FVertical = F × sin(θ), where F is the magnitude of the push force (140 N) and θ is the angle at which it is applied (20°). So, FVertical = 140 N × sin(20°) = 47.77 N.

3. FNormal: The normal force exerted by the floor on the box is equal in magnitude and opposite in direction to the vertical component of the applied force. So, FNormal = -FVertical = -47.77 N.

Therefore, the magnitude of FNormal on the box from the Earth is 47.77 N.

To find the magnitude of the normal force on the box from Earth, we need to consider the forces acting on the box in the vertical direction.

The normal force is the force exerted by a surface perpendicular to the surface. In this case, it is the force exerted by the floor on the box. The normal force is equal in magnitude and opposite in direction to the force exerted by the box on the floor due to gravity.

In this problem, the box is at rest on a level floor. So, the upward force exerted by the floor (normal force) should be equal to the downward force of gravity acting on the box.

The force due to gravity can be calculated using the equation:

Fgravity = m * g

where m is the mass of the box (13 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Fgravity = 13 kg * 9.8 m/s^2
Fgravity = 127.4 N

Since the box is at rest, the upward normal force should be equal to the force due to gravity:

FNormal = Fgravity
FNormal = 127.4 N

Therefore, the magnitude of the normal force on the box from Earth is 127.4 Newtons.