Question

A sport utility vehicle (SUV) and a sports car travel around thesame horizontal curve. The SUV has a static stability factor of0.70 and can negotiate the curve at amaximum speed of 14 m/s withoutrolling over. The sports car has a static stability factor of1.5. At what maximum speed (inm/s) can the sports car negotiate the curve without rollingover?

Answer 1

The sports car, with a static stability factor of 1.5, can negotiate the curve at a maximum speed of approximately 18.7 m/s without rolling over.

Step-by-step explanation:

To find the maximum speed at which the sports car can negotiate the curve without rolling over, we'll use the static stability factor (SSF) which is a measure of a vehicle's resistance to rollover in a turn. This factor is essentially the ratio of the height of the center of gravity to half the track width of the vehicle. The greater the SSF, the higher the speed at which the vehicle can safely negotiate a curve without rolling over.

The SUV, with an SSF of 0.70, can negotiate the curve at a maximum speed of 14 m/s. Since the SSF is directly proportional to the maximum speed squared, we can set up a proportion to solve for the unknown speed of the sports car with an SSF of 1.5 using the SUV's known values.

The formula looks like this:

(Sports car speed / SUV speed)^2 = Sports car SSF / SUV SSF

Substituting the known values, we get:

(Sports car speed / 14 m/s)^2 = 1.5 / 0.70

Solving for the sports car speed, we find:

Sports car speed = 14 m/s * √(1.5 / 0.70)

Sports car speed ≈ 18.7 m/s

Thus, the sports car can negotiate the curve at a maximum speed of approximately 18.7 m/s without rolling over.

Answer 2

To find the maximum speed at which the sports car can negotiate the curve without rolling over, the static stability factors of both vehicles are used to set up a proportion. By performing the calculation, the sports car can do so at approximately 20.5 m/s.

Step-by-step explanation:

The question is asking at what maximum speed can the sports car negotiate the curve without rolling over, given that the SUV can do so at 14 m/s with a static stability factor of 0.70, and the sports car has a static stability factor of 1.5.

The static stability factor (SSF) determines a vehicle's stability in a turn and is directly related to the risk of rollover. It's defined by the height of the center of gravity divided by half the track width of the vehicle. A higher SSF indicates a lower risk of a rollover.

To find the maximum speed for the sports car, we can set up a proportion since the maximum speed depends on the square root of the SSF: vcar/vSUV = sqrt(SSFcar/SSFSUV). Plugging in the values gives us vcar = 14 m/s * sqrt(1.5/0.70), which we can calculate.

Performing the calculation, we have vcar = 14 m/s * sqrt(1.5/0.70) = 14 m/s * sqrt(2.1429) = 14 m/s * 1.4639 ≈ 20.5 m/s. Thus, the sports car can negotiate the curve at a maximum speed of approximately 20.5 m/s without rolling over.