Hi everyone, finished all my utexas physics homework, save this last question... I don't quite why I'm not getting the right answer. Any help offered will be appreciated, it could lead me to the right answer :)
P.S.---- I've already imputed the following four answers which were incorrect. (3844N,8487N,11194N,12925N)
The next curve that the car approaches also
has a radius of curvature 67.4 m. It is banked
at an angle of 30◦. The ideal speed for this
curve is vc (banked so that the car experiences
no frictional force). The speed of the car vs as
it rounds this curve is vs = 0.673 vc.
If the mass of the car is 1500 kg, what is
the magnitude of the frictional force needed
to keep it from sliding sideways?
Answer in units of N.
To find the magnitude of the frictional force needed to keep the car from sliding sideways, we can use the concept of centripetal force.
When a car is moving in a circle of radius r with a speed v, the net force acting on the car is the centripetal force. In this case, the centripetal force is provided by the frictional force between the tires of the car and the road.
The centripetal force can be calculated using the following formula:
F = (m * v^2) / r
where F is the centripetal force, m is the mass of the car, v is the velocity of the car, and r is the radius of curvature of the curve.
First, let's find the velocity of the car (v) as it rounds the curve:
vs = 0.673 vc
We need to find vc, which is the ideal speed for the curve where the car experiences no frictional force. The ideal speed can be calculated using the following formula:
vc = sqrt(g * r * tan(theta))
where g is the acceleration due to gravity and theta is the angle of banking.
Plugging in the values:
g = 9.8 m/s^2 (approximate value for Earth's gravity)
r = 67.4 m
theta = 30 degrees (convert to radians: theta = 30 * pi/180)
vc = sqrt(9.8 * 67.4 * tan(30 * pi/180))
Compute the value of vc using a calculator and then substitute the value of vc into the equation for vs to find the velocity of the car (v) as it rounds the curve.
Once you have the value of v, you can compute the centripetal force (F) using the formula mentioned earlier:
F = (m * v^2) / r
Substituting the values of m, v, and r, calculate the centripetal force, which is also the magnitude of the frictional force needed to keep the car from sliding sideways.