Question

The same car now travels on a straight track and goes over a hill with radius 101 m at the top. What is the maximum speed that the car can go over the hill without leaving the road?

Answer 1

The maximum speed at which a car can go over a hill with radius 101 m without leaving the road is approximately 31.47 m/s. This is calculated using the gravitational force as the centripetal force required for circular motion at the top of the hill.

Step-by-step explanation:

To find the maximum speed at which a car can go over a hill with radius 101 m without leaving the road, we must consider the condition where the gravitational force is the only force providing the centripetal force required for circular motion at the top of the hill. When the car is on the verge of leaving the road, the normal force is zero, and the gravitational force (mg, where m is the mass of the car and g is the acceleration due to gravity) provides the necessary centripetal force (mv²/r, where v is the velocity of the car and r is the radius of the hill). Therefore, the maximum speed v can be calculated using the equation:

mg = mv²/r

After canceling out the mass m from both sides of the equation, we get:

v² = rg

v = √(rg)

Substituting the given values (r = 101 m and g = 9.8 m/s²), we get:

v = √(101 m * 9.8 m/s²)

v ≈ √(989.8 m²/s²)

v ≈ 31.47 m/s

Thus, the maximum speed is approximately 31.47 m/s.

Answer 2

The maximum speed of the car is 31.46 m/s.

Step-by-step explanation:

Given that,

Radius = 101 m

We need to calculate the maximum speed that the car can go over the hill without leaving the road

Using relation of normal force and centripetal force

`(mv^2)/(r)=mg`

Where, m = mass of car

`v=√(rg)`

Put the value into the formula

`v=√(101*9.8)`

`v=31.46\ m/s`

Hence, The maximum speed of the car is 31.46 m/s.