The angle with respect to the horizontal axis is 13 degrees.
What is the net force?
The net force is the vector sum of all the forces that act upon an object.
Given that the puck is moving at a speed of 30.6 m/s and the radius of the track is 414 m. The angle with respect to the horizontal axis is ϕ.
The attachment shows the forces acted on the puck in all directions.
There is no motion in the vertical direction, so the net force in the vertical direction is given as,
[tex]N cos \phi - mg = 0[/tex]
[tex]N cos \phi = mg[/tex]
[tex]N = \dfrac {mg}{cos\phi}[/tex]
Where g is gravitation acceleration and m is the mass of the puck.
The force in the horizontal axis is given as [tex]N sin \phi[/tex]. This force provides the necessary centripetal force to move around the circular track. So,
[tex]N sin\phi = \dfrac {mv^2}{r}[/tex]
Where v is the speed of the puck and r is the radius of the track.
Substituting the value of N, we get.
[tex]\dfrac {mg}{cos \phi} \times sin \phi = \dfrac {mv^2}{r}[/tex]
[tex]tan \phi = \dfrac {v^2}{rg}[/tex]
[tex]\phi = tan^{-1} \dfrac {30.6^2}{414 \times 9.8}[/tex]
[tex]\phi = 13^\circ[/tex]
Hence we can conclude that the angle with respect to the horizontal axis is 13 degrees.
To know more about the net force, follow the link given below.
https://brainly.com/question/16985000.
