A car going 30 m/s just barely makes it around a curve without skidding. This curve had a radius of 150 m. The next curve has a radius of 75 m. At what maximum velocity can it go around this curve without skidding?

v1²/R1=v2²/R2,

v2=sqrt(v1²•R2/R1)=

To determine the maximum velocity at which a car can go around a curve without skidding, we need to consider the centripetal force and compare it to the maximum frictional force that can be exerted between the car's tires and the road.

The centripetal force required to keep the car moving in a circular path is given by the formula:

F = (m * v^2) / r

Where:
- F is the centripetal force
- m is the mass of the car
- v is the velocity of the car
- r is the radius of the curve

The maximum frictional force between the tires and the road is given by the formula:

F_friction = m * g * µ

Where:
- F_friction is the maximum frictional force
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- µ is the coefficient of friction between the tires and the road

To find the maximum velocity at which the car can go around the second curve without skidding, we need to equate the two forces:

F = F_friction

Substituting the formulas for F and F_friction:

(m * v^2) / r = m * g * µ

Simplifying the equation:

v^2 = r * g * µ

Solving for v:

v = √(r * g * µ)

Now let's calculate the maximum velocity for the second curve using the given radius of 75 m. The coefficient of friction, µ, is typically between 0 and 1, with higher values indicating greater friction between the tires and the road.

Let's assume a conservative value of µ = 0.7. Therefore, the maximum velocity is:

v = √(75 * 9.8 * 0.7)
v = √(514.5)
v ≈ 22.7 m/s (rounded to one decimal place)

Hence, the car can go around the second curve without skidding at a maximum velocity of approximately 22.7 m/s.