A car of mass MMM = 1500 kgkg traveling at 60.0 km/hourkm/hour enters a banked turn covered with ice. The road is banked at an angle 20 degrees, and there is no friction between the road and the car's tires. What is the radius rrr of the turn if θθtheta = 20.0 ∘∘ (assuming the car continues in uniform circular motion around the turn)? Now, suppose that the curve is level (θ=0) and that the ice has melted, so that there is a coefficient of static friction μμmu between the road and the car's tires. What is μminμminmu_min, the minimum value of the coefficient of static friction between the tires and the road required to prevent the car from slipping? Assume that the car's speed is still 60.0 km/hourkm/hour and that the radius of the curve is 77.9 mm.
Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
A car of mass MMM = 1500 kgkg traveling at 60.0 km/hourkm/hour enters a banked turn covered with ice. The road is banked at an angle 20 degrees, and there is no friction between the road and the car's tires.
What is the radius rrr of the turn if θθtheta = 20.0 ∘∘ (assuming the car continues in uniform circular motion around the turn)?
Now, suppose that the curve is level (θ=0) and that the ice has melted, so that there is a coefficient of static friction μμmu between the road and the car's tires. What is μminμminmu_min, the minimum value of the coefficient of static friction between the tires and the road required to prevent the car from slipping? Assume that the car's speed is still 60.0 km/hourkm/hour and that the radius of the curve is 77.9 mm.
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