How much friction force will be required if a car weighing 2100kg traveling at 28m/s rounds a curve of radius 59m banked at a 15 degree angle
To calculate the friction force required for a car rounding a banked curve, we need to take into account the gravitational force and the centripetal force.
1. Calculate the gravitational force acting on the car:
Gravitational force = mass * acceleration due to gravity
Gravitational force = 2100 kg * 9.8 m/s^2
Gravitational force = 20580 N
2. Calculate the centripetal force required to keep the car moving in a curved path:
Centripetal force = (mass * velocity^2) / radius
Centripetal force = (2100 kg * (28 m/s)^2) / 59 m
Centripetal force = 26428.81 N
3. Calculate the horizontal component of the gravitational force:
Horizontal component of gravitational force = Gravitational force * sin(angle)
Horizontal component of gravitational force = 20580 N * sin(15°)
Horizontal component of gravitational force = 5347.66 N
4. Calculate the net force required to provide the centripetal force:
Net force = Centripetal force - Horizontal component of gravitational force
Net force = 26428.81 N - 5347.66 N
Net force = 21081.15 N
5. Calculate the frictional force required to provide the net force:
Frictional force = Net force
Frictional force = 21081.15 N
Therefore, the friction force required is approximately 21081.15 N.
To calculate the friction force required for the car to round the curved track, we need to consider both the gravitational force component pulling the car down the slope and the centripetal force required to keep the car moving in a circular path.
First, let's find the gravitational force component acting on the car. This force can be calculated using the formula:
F_grav = m * g * sin(theta)
where:
m = mass of the car = 2100 kg
g = acceleration due to gravity = 9.8 m/s^2
theta = angle of the banked curve = 15 degrees
Substituting the values:
F_grav = 2100 kg * 9.8 m/s^2 * sin(15 degrees)
Next, let's calculate the centripetal force required to keep the car moving in a circular path. The centripetal force can be calculated using the formula:
F_cen = (m * v^2) / r
where:
m = mass of the car = 2100 kg
v = velocity of the car = 28 m/s
r = radius of the curve = 59 m
Substituting the values:
F_cen = (2100 kg * (28 m/s)^2) / 59 m
Now, the required friction force is equal to the difference between the centripetal force and the gravitational force acting on the car:
Friction force = F_cen - F_grav
Substituting the previously calculated values:
Friction force = [(2100 kg * (28 m/s)^2) / 59 m] - [2100 kg * 9.8 m/s^2 * sin(15 degrees)]
Finally, evaluate this expression to find the friction force required for the car to round the curve.