Newton's second law, kinematics and graphic analysis we can find the results for the questions about the movement of the trine are:
Newton's second law establishes a relationship between the net force, the mass and the acceleration of the body. In the attachment we can see a free body diagram which is a schematic of the forces without the details of the bodies.
N-W = 0
fr = ma
where N is the normal, W the weight of the body, fr the friction force, m the mass and a the acceleration
The friction force is a macroscopic representation of the interactions between the two surfaces, it is given by the expression
fr = μ N
where μ is the coefficient of friction between the two surfaces.
We substitute
μ mg = m a
a = μ g
Kinematics study the movement of bodies, looking for relationships between position, speed and acceleration.
v= v₀ – at t
In this case they give tables and graphs with the values of time and speed, where we can see that the relationship is a straight line that has as equation
y = ax +b
Where y is the dependent variable, x is the independent variable, a is the slope, and b is the cutoff point.
If we relate the two equations:
a = mug
μ = [tex]\frac{a}{g}[/tex]
Using linear regression the slope and cutoff point is:
The man.
The slope is a = -0.8 m/s² and the cut-off point b= 4.86 m/s.
Let's calculate the coefficient of friction.
μ = [tex]\frac{0.8}{9.8}[/tex]
μ = 0.082
The child.
The slope is a = -0.98 m/s² and the cut-off point b= 4.72 m/s.
We calculate the coefficient of friction.
μ = [tex]\frac{0.98}{9.8}[/tex]
μ = 0.1
The relationship between the two coefficients of friction is
[tex]\frac{\mu_{man} }{\mu_{boy}} = \frac{0.082}{0.1}[/tex]
[tex]\frac{\mu_{man}}{\mu_{boy}} = 0.82[/tex]
The results are very exact since there are values of several points in the route and the graphical analysis gives the best possible value for all the points.
There are some variables not taken into account, one of the most important is friction with the wind and wind speed.
In conclusion using Newton's second law, kinematics and graphic analysis we can find the results for the questions about the movement of the trine are:
Learn more about kinematics and graphical analysis here: brainly.com/question/11579754
