Respuesta :
Given:
Weight = 14000 N
Velocity = 25 m/s
Radius of curve = 200 m
Let's find the magnitude of the net force of the car that is keeping it moving in a circle.
Let's first find the centripetal acceleration:
[tex]a_c=\frac{v^2}{r}[/tex]Where:
v = 25 m/s
r = 200 m
We have:
[tex]\begin{gathered} a_c=\frac{25^2}{200} \\ \\ a_c=\frac{625}{200} \\ \\ a_c=3.125\text{ m/s}^2 \end{gathered}[/tex]Now, to find the force, apply the formula:
[tex]F=m*a_c[/tex]Where:
m is the mass of the car
To find the mass of the car, we have:
[tex]\begin{gathered} m=\frac{F}{g} \\ \\ Where:g=9.8\text{ m/s}^2 \\ \\ m=\frac{14000}{9.8}=1428.57\text{ kg} \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} F_c=m*a_c \\ \\ F_c=1428.57*3.125 \\ \\ F_c=4464.29\text{ N} \end{gathered}[/tex]Therefore, the magnitude of the net force that is keeping the car moving in a circle is 4464.29 N.
ANSWER:
4464.29 N
