Newton's second law allows finding the result for the angle where the block begins to slide is:
θ = 21.8º
Newton's second law gives the relationship between the force, mass and acceleration of bodies.
Σ F = m a
Where bold indicates vectors, F is force, m is mass, and acceleration.
In the inclined plane exercises, the reference hiss with respect to which to make the measurements is the x-axis parallel to the plane and the positive direction in the direction of movement, the y-axis perpendicular to the plane.
In the attached we have a free body diagram of the system, let's use trigonometry to descompose the weight of the body.
cos θ = [tex]\frac{W_y}{W}[/tex]
sin θ = [tex]\frac{W_x}{W}[/tex]
[tex]W_y[/tex] = W cos θ
Wₓ = W sin θ
The friction is a force that opposes movement and its expression is
fr = μ N
Where fr is the friction force, N the normal of the surface and μ is a coefficient that takes different values. It is static if is not relative motion between the two surfaces and Dinamic si exsit relative movimient.
Let's apply Newton's second law to each axis.
y-axis
N- [tex]W_y[/tex] = 0
N = W cos θ
x-axis
Wₓ - fr = m a
Let's substitute.
W sin θ - μ W cos θ = m a
g (sin θ - μ cos θ) = a
They ask the angle with which it begins to slide, this is the point before beginning to slide between the two surfaces there is no relative movement, so the friction coefficient is static, let's write the equation.
g (sin θ - μ cos θ) = 0
[tex]\frac{sin \theta}{ cos \theta} = \mu[/tex]
tan θ = μ
θ = tan⁻¹ μ
Let's calculate.
θ = tan⁻¹ 0.40
θ = 21.8º
When it begins to slide there is a relative movement between the two surfaces and the friction coefficient becomes dynamic and to continue at a constant speed the angle must be decreased.
In conclusion using Newton's second law we can find the angle for the motion to begin is:
θ = 21.8º
Learn more here: brainly.com/question/6821567
