a car with a mass of 1,500 kg requires a centripetal force of 640 n to safely follow a circular curve in the…

a car with a mass of 1,500 kg requires a centripetal force of 640 n to safely follow a circular curve in the road at 13.4 m/s. what is the radius of the curve? o 31 m o 77 m o 421 m o 860 m

a car with a mass of 1,500 kg requires a centripetal force of 640 n to safely follow a circular curve in the road at 13.4 m/s. what is the radius of the curve? o 31 m o 77 m o 421 m o 860 m

Answer

Explanation:

Step1: Recall centripetal - force formula

The centripetal - force formula is $F = \frac{mv^{2}}{r}$, where $F$ is the centripetal force, $m$ is the mass of the object, $v$ is the velocity, and $r$ is the radius of the circular path. We need to solve for $r$.

Step2: Rearrange the formula for $r$

From $F=\frac{mv^{2}}{r}$, we can get $r=\frac{mv^{2}}{F}$.

Step3: Substitute the given values

Given $m = 1500\ kg$, $v = 13.4\ m/s$, and $F = 640\ N$. First, calculate $v^{2}=(13.4)^{2}=179.56$. Then $mv^{2}=1500\times179.56 = 269340$. Now, $r=\frac{269340}{640}\approx421\ m$.

Answer:

421 m