Two banked curves have the same radius. Curve A is banked at 10.9 °, and curve B is banked at an angle of 18.8 °. A car can travel around curve A without relying on friction at a speed of 17.1 m/s. At what speed can this car travel around curve B without relying on friction?
if no friction is involved in the force balance, we know the
horizontal component of the normal force must equal the centripetal
force; this component has magnitude Nsin(theta)=mv^2/r
the vertical component of N must equal the weight of the car, or
Ncos(theta)=mg
divide these two relations to get tan(theta) =v^2/rg or v^2= r g
tan(theta)
now, we know that when theta=14 deg v=18m/s, so we have
tan10.9=17.1^2/(rg) =>r=154.94m
now, find v^2 when theta=18.8 deg
v^2=154.94m x 9.8m/s/s x tan18.8 => v=22.73m/s
we know,
tan(theta) = v^2(g*r)
tan(theta_A) = Va^2/(g*r) --(1)
tan(theta_B) = Vb^2/(g*r) --(2)
devide eqn 2 with eqn 1
tan(theta_B)/tan(theta_A) = (Vb/Va)^2
vb = va*sqrt( tan(theta_B)/tan(theta_A))
= 17.1*sqrt(tan(18.8)/tan(10.9))
= 22.74 m/s
Two banked curves have the same radius. Curve A is banked at 10.9 °, and curve...
A car rounds a curve that is banked inward. The radius of curvature of the road is R = 140 m, the banking angle is θ = 26°, and the coefficient of static friction is μs = 0.39. Find the minimum speed that the car can have without slipping. A car rounds a curve that is banked inward. The radius of curvature of the road is R 140 m, the banking angle is 26e, and the coefficient of static minimum...
Two curves on a highway have the same radii. However, one is unbanked and the other is banked at an angle of degrees. A car can safely travel along the unbanked curve at a maximum speed under conditions when the coefficient of static friction between the tures and the road is . The banked curve is frictionless, and the car can negotiate it at the same maximum speed . Find the coefficient of static friction between the tires and the...
Consider the motion of a car around a banked curve. The angle of the bank with respect to the horizontal is 15.0 degrees, the speed of the car is 20.0 m/s, the radius of curvature for the curve is 30.0 m, and the coefficient of static friction is 0.500. The mass of the car is 1000 kg. a) What is the frictional force? b) Is there a speed at which the frictional force would be zero? If so, what is...
A car rounds a curve that is banked inward. The radius of curvature of the road is R = 142 m, the banking angle is θ = 30°, and the coefficient of static friction is μs = 0.32. Find the minimum speed that the car can have without slipping. I got 36.5196 m/s, which isn't correct.
A highway curve of radius 70 m is banked at a 15° angle. At what speed vo can a car take this curve without assistance from friction?
A car rounds a curve that is banked inward. The radius of curvature of the road is R = 152 m, the banking angle is θ = 32°, and the coefficient of static friction is μs = 0.23. Find the minimum speed that the car can have without slipping.
1) At what angle should a curve of radius 170 m be banked, so cars can travel safely at 55 mi/h without relying on friction? 2)The system shown is moving down the incline with contant veloicty. If M = 10 kg and m= 54 kg and an incline angle is 300 between the block M and the incline? with steps please
A car goes around a curve on a road that is banked at an angle of 33.5 degree. Even though the road is slick, the car will stay on the road without any friction between its tires and the road when its speed is 23.0 m/s. Part A What is the radius of the curve?
highway curves are often banked, so the normal force provides the centripetal force and cars don’t have to rely on friction. After having responded to an emergency call in the middle of a snowstorm, an ambulance is speeding back towards the hospital along a slippery curved road. Your job is to inform the ambulance driver of the maximum speed at which he can travel around this curve without slipping up the bank. You are told that the curve has a...
A concrete highway curve of radius 70.0 m is banked at a 19.0° angle. What is the maximum speed with which a 1900 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.)