A 905 kg test car travels around a 3.34 km circular track. If the magnitude of the force that maintains the car’s circular motion is 2134 N, what is the car’s tangential speed? Answer in units of m/s.
Ac = v^2/R
m Ac = m v^2/R = 2134
so
905 v^2/R = 2134
but 2 pi R = 3340 so R = 3340/2pi
so
905 * 2 * pi * v^2 = 2134 * 3340
Hey what? circumference = 2 pi R :)
To find the car's tangential speed, we need to use the equation:
Force = mass * tangential speed^2 / radius
In this case, the force that maintains the car's circular motion is given as 2134 N, the mass of the car is 905 kg, and the radius of the circular track is determined by the circumference, which is 2 * π * radius = 3.34 km.
To find the radius, we can rearrange the equation:
Circumference = 2 * π * radius
3.34 km = 2 * π * radius
Now, we can solve for the radius:
radius = (3.34 km) / (2 * π)
Finally, we can substitute the values into the original equation and solve for the tangential speed:
2134 N = (905 kg) * tangential speed^2 / (3.34 km)