A 1200 kg car rounds a curve of radius 71 m banked at an angle of 11°. What is the magnitude of the friction force required for the car to travel at 82 km/h?
My physics optional extra work: This would be helpful so I can compare the solutions here as I do the work by myself.
Wow!
Nine posts in seven minutes! Must be a record!!
To find the magnitude of the friction force required for the car to travel at 82 km/h around a banked curve, let's go through the steps:
1. Convert the speed from km/h to m/s:
Divide the given speed by 3.6 (since there are 3.6 meters in 1 second).
82 km/h = (82 / 3.6) m/s = 22.78 m/s.
2. Calculate the centripetal force acting on the car:
The centripetal force is the force that keeps an object moving in a curved path and is given by the equation:
F_c = (m * v^2) / r,
where m is the mass of the car, v is the velocity of the car, and r is the radius of the curve.
F_c = (1200 kg * (22.78 m/s)^2) / 71 m.
3. Determine the angle of the banking:
The angle of the banking is given as 11°.
4. Calculate the normal force:
The normal force, N, is the perpendicular force exerted by a surface to support the weight of an object resting on it. In this case, it is equal to the vertical component of the car's weight.
N = m * g,
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
N = 1200 kg * 9.8 m/s^2.
5. Find the friction force:
To keep the car moving in a circular path on the banked curve, the friction force, F_f, must act inward and provide the necessary centripetal force.
F_f = F_c * sin(θ),
where θ is the angle of banking in radians.
Now, let's put the values into the equations:
F_c = (1200 kg * (22.78 m/s)^2) / 71 m,
N = 1200 kg * 9.8 m/s^2, and
F_f = F_c * sin(11°).
By substituting the given values into these equations, you can calculate the magnitude of the friction force required for the car to travel at 82 km/h.