When you're driving your 1200-kg car, you go around a corner of radius 60.8 m. The coefficient of static friction between the car and the road is 0.67. Assuming your car doesn't skid, what is your speed if the force exerted on it is 5800N?
Net force F= F(fr) - mv²/R =μmg - mv²/R
mv²/R = μmg – F.
Solve for v
To find the speed of the car, we need to use the equation that relates the friction force to the centripetal force.
The friction force between the car's tires and the road provides the centripetal force needed to keep the car moving in a curved path. The equation for centripetal force is:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the car
v is the speed of the car
r is the radius of the corner
In this case, the force exerted on the car is given as 5800 N, the mass of the car is 1200 kg, and the radius is 60.8 m.
We can rearrange the equation to solve for v:
v^2 = (F * r) / m
v = √((F * r) / m)
Now, let's plug in the values and calculate:
v = √((5800 N * 60.8 m) / 1200 kg)
First, multiply 5800 N and 60.8 m:
v = √(352640 N·m / 1200 kg)
Divide by 1200 kg:
v = √(293.87 N·m/kg)
Finally, take the square root:
v ≈ 17.13 m/s
Therefore, your speed, assuming the car doesn't skid, would be approximately 17.13 m/s.