Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

A car of mass M = 1000 kg traveling at 50.0 km/hour enters a banked turn covered with ice. The road is banked at an angle θ , and there is no friction between the road and the car's tires as shown in (Figure 1). Use g = 9.80 m/s2 throughout this problem.What is the radius r of the turn if θ = 20.0 ∘ (assuming the car continues in uniform circular motion around the turn)?

Sagot :

onyebuchinnaji

The radius of the curved road at the given condition is 54.1 m.

The given parameters:

  • mass of the car, m = 1000 kg
  • speed of the car, v = 50 km/h = 13.89 m/s
  • banking angle, θ = 20⁰

The normal force on the car due to banking curve is calculated as follows;

[tex]Fcos(\theta) = mg[/tex]

The horizontal force on the car due to the banking curve is calculated as follows;

[tex]Fsin(\theta) = \frac{mv^2}{r}[/tex]

Divide the second equation by the first;

[tex]\frac{Fsin(\theta)}{Fcos(\theta) } = \frac{mv^2}{rmg} \\\\tan(\theta) = \frac{v^2}{rg} \\\\r = \frac{v^2}{g \times tan(\theta)} \\\\r = \frac{13.89^2}{9.8 \times tan(20)} \\\\r = 54.1 \ m[/tex]

Thus, the radius of the curved road at the given condition is 54.1 m.

Learn more about banking angle here: https://brainly.com/question/8169892

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.