A 150-newton force, applied to a wooden crate at an angle of 30° above the horizontal, causes the crate to travel at constant velocity across a horizontal wooden floor.
1. Calculate the magnitude of the normal force exerted by the floor on the crate. [Show all work, including the equation and substitution with units.]=

Newton's second law establishes a relationship between the force, the mass and the acceleration of bodies, in the special case that the acceleration is zero, it is called a mechanical equilibrium condition.

∑ F = 0

A free body diagram is a diagram of the forces without the details of the bodies, in the attachment we can see this diagram, let's write the equilibrium condition for each axis.

x- axis

Fₓ -fr = 0

y-axis

F_y + N – W =0

Let's use trigonometry to find the components of the applied force.

Cos 30= [tex]\frac{F_x}{F} [/tex]

sin 30 = [tex]\frac{F_y}{F } [/tex]

Fₓ = F cos 30

[tex]F_y[/tex] = F sin 30

The weight of a body is the mass times the acceleration due to gravity.

W = m g

Let's substitute.

F sin 30 + N – m g = 0

N= m g – F sin 30

Let's calculate.

N = m 9.8 – 150 sin 30

N = m 9.8 - 75

To finish the calculation, the mass of the body must be known, suppose a value of 10 kg.

N=10 9.8 -75

N = 23N

In conclusion using the mechanical equilibrium condition we can find the value of the normal for the body is:

The normal is N = 23 N

Learn more about the mechanical equilibrium condition here: brainly.com/question/12804448