3 questions about Normal force equation

1. A block has a mass of 5 kg. If g = 10 m/s^{2}, determine:

a) the weight of the block

b) the normal force if the block is placed on a flat plane

c) the normal force if the block rests on an inclined plane that forms an angle of 30^{o} to the horizontal

__Known:__

The mass of the block (m) = 5 kg

Acceleration due to gravity (g) = 10 m/s^{2}

__Wanted:__ w, N on the plane and N on the incline

__Solution:__

a) Beam weight

w = m g = 5 (10) = 50 Newton

b) The normal force if the block is in a flat plane

N = w = 50 Newton

c) The normal force if the block is on an inclined plane

N = w_{y} = w cos θ = 50 (cos 30) = 50 (½ √3) = 25√3 Newton

2. A 120 gram eraser is pressed perpendicularly to the board with a force of 15 N. What is the normal force acting on the eraser?

__Known____:__

Mass (m) = 120 grams = 0.12 kg

Force (F) = 15 Newton

__Wanted:__ Normal force

__Solution:__

Normal force = thrust = 15 Newton

3. Bottled drinking water that is still in the box is pulled with a force of F = 200 N which forms an angle of 37^{o} with the horizontal. Sin 37^{o} = 0.6. The mass of the cardboard and its contents is 20 kg. If the coefficient of static friction on the floor is 0.5 and the coefficient of kinetic friction on the floor is 0.2, determine the normal force acting on the cardboard.

__Known:__

Pull force (F) = 200 N

Sin 37 = 0,6

Fy = F sin 37 = (200)(0,6) = 120 N

Cardboard mass (m) = 20 kg

The weight of the cardboard (w) = m g = (20)(10) = 200 N

__Wanted:__ Normal force on cardboard (N)

__Solution:__

Calculate the normal force using the normal force formula:

N = w – F_{y }= 200 – 120 = 80 Newton