A car is traveling around a bend at a speed of 12.4 m/s. The bend has a radius of curvature of 66.7 m. Friction is the only force acting towards the center of the circle. If the mass of the car is 862 kg, what is the force of friction required to make the car go around the bend?
F(fr)=ma=mv²/R=
= 862•(12.4)²/66.7 = 160.25 N
To find the force of friction required to make the car go around the bend, we need to use the centripetal force equation.
The centripetal force is given by the equation:
F = (m * v^2)/r
Where:
F = centripetal force
m = mass of the car
v = velocity of the car
r = radius of curvature
In this case:
m = 862 kg
v = 12.4 m/s
r = 66.7 m
Now, let's plug in the values into the equation and solve for F:
F = (862 kg * (12.4 m/s)^2) / 66.7 m
First, let's square the velocity:
(12.4^2) = 153.76
Now, let's calculate the force of friction:
F = (862 kg * 153.76) / 66.7 m
F = 19835.12 kg*m/s^2 / 66.7 m
F ≈ 297.39 kg*m/s^2
Therefore, the required force of friction to make the car go around the bend is approximately 297.39 kg*m/s^2.