Curve A is banked at 11.2 °, and curve B is banked at an angle of 15.2 °. A car can travel around curve A without relying on friction at a speed of 14.5 m/s. At what speed can this car travel around curve B without relying on friction?
Do I need to find radius in order to solve for this one, I'm kinda lost please advice.
I was able to solve this problem
at firs, use the equation V=sqrt(R g tan theta)
since you have two angles you will need to separate the equation into 2
Va= sqrt(r g tan a theta)
Vb= sqrt (r g tan b theta)
then solve for Vb
Vb/Va= sqrt(r g tanb )/ sqrt(r g tan a theta)
r and g will cross out
therefore, Vb= sqrt( tan b theta)/ sqrt(tan a theta)* Va
So the answer should be:
Vb= sqrt tan 15.2/ sqrt tan 11.2* 14.5
vb= 16.99 m/s or 17 m/s
To determine the speed at which the car can travel around curve B without relying on friction, it is indeed necessary to find the radius of the curve. Here's how you can solve the problem:
1. Start by drawing a diagram of the situation. Label curve A with its given angle of 11.2° and curve B with its given angle of 15.2°.
2. Next, recall the formula for the banking angle, which relates the speed of the car, the angle of the curve, and the radius of the curve:
tan(θ) = (v^2) / (g * r)
where θ is the angle of the curve, v is the speed of the car, g is the acceleration due to gravity (approximately 9.8 m/s^2), and r is the radius of the curve.
3. Rearrange the equation to solve for the radius, r:
r = (v^2) / (g * tan(θ))
4. Plug in the values for curve A, with θ = 11.2°, v = 14.5 m/s, and g = 9.8 m/s^2, to calculate the radius of curve A.
r_A = (14.5^2) / (9.8 * tan(11.2°))
5. Once you have calculated the radius for curve A, you can use the same formula to find the speed at which the car can travel around curve B without relying on friction.
r_B = (v_B^2) / (9.8 * tan(15.2°))
Rearrange this equation to solve for v_B:
v_B = sqrt(r_B * 9.8 * tan(15.2°))
6. Now, substitute the value of radius r_B with the previously calculated value for curve A, and solve for v_B:
v_B = sqrt(r_A * 9.8 * tan(15.2°))
7. Plug in the value of r_A calculated in step 4, along with the given values of g = 9.8 m/s^2 and θ = 15.2°, and calculate the speed v_B.
v_B = sqrt(r_A * 9.8 * tan(15.2°))
By following these steps, you should be able to find the speed at which the car can travel around curve B without relying on friction.