Complete Question
The cars of a roller-coaster ride have a speed of 19.0 km/h as they pass over the top of the circular track. Neglect any friction and calculate their speed v when they reach the horizontal bottom position. At the top position, the radius of the circular path of their mass centers is 21 m, and all six cars have the same mass.V = -18 m What is v?X km/h
Answer:
[tex]v=23.6m/s[/tex]
Explanation:
Velocity [tex]v_c=18.0km/h[/tex]
Radius [tex]r=21m[/tex]
initial velocity u[tex]u=19=>5.27778[/tex]
Generally the equation for Angle is mathematically given by
[tex]\theta=\frac{v_c}{2r}[/tex]
[tex]\theta=\frac{18}{2*21}[/tex]
[tex]\theta=0.45[/tex]
[tex]\theta=25.7831 \textdegree[/tex]
Generally
Height of mass
[tex]h=\frac{rsin\theta}{\theta}[/tex]
[tex]h=\frac{21sin25.78}{0.45}[/tex]
[tex]h=20.3m[/tex]
Generally the equation for Work Energy is mathematically given by
[tex]0.5mv_0^2+mgh=0.5mv^2[/tex]
Therefore
[tex]v=\sqrt{u^2+2gh}[/tex]
[tex]v=\sqrt{=5.27778^2+2*9.81*20.3}[/tex]
[tex]v=23.6m/s[/tex]
