a car weighing 15000N rounds a curve of 60m. radius banked at angle of 30 degrees.find the frictional force acting on the tires when the car is travelling at 100kph.The coefficient of friction between the tires and the road is 0.90.
S=2.74
To find the frictional force acting on the tires, we can follow these steps:
Step 1: Find the vertical force acting on the car due to its weight.
Given: Weight of the car = 15000 N
The vertical force acting on the car is equal to its weight. So, the vertical force (Fn) = 15000 N.
Step 2: Find the centripetal force required for the car to move in a curve.
Given: Radius of the curve (r) = 60 m
The centripetal force (Fc) is given by the formula: Fc = (m * v^2) / r
Here, m is the mass of the car (which we can find using weight), and v is the velocity of the car.
Step 3: Find the mass of the car.
Given: Weight of the car = 15000 N
The weight of the car is given by the formula: Weight = mass * gravity (where gravity = 9.8 m/s^2)
So, mass = Weight / gravity = 15000 N / 9.8 m/s^2
Step 4: Convert the velocity from km/h to m/s.
Given: Velocity of the car = 100 km/h
We need to convert it to m/s, so, Velocity (v) = (100 km/h) * (1000 m/km) / (3600 s/h)
Step 5: Calculate the centripetal force.
Plug in the values of mass (from Step 3) and velocity (from Step 4) into the formula: Fc = (m * v^2) / r
Step 6: Calculate the frictional force.
The frictional force (Ff) can be calculated as Ff = coefficient of friction * vertical force (Fn)
Let's do the calculations:
Step 1: Fn = 15000 N
Step 2: Fc = (m * v^2) / r
Step 3: mass = Weight / gravity = 15000 N / 9.8 m/s^2
Step 4: v = (100 km/h) * (1000 m/km) / (3600 s/h)
Step 5: Fc = (mass * v^2) / r
Step 6: Ff = coefficient of friction * Fn
Now, let's calculate the values:
Step 1:
Fn = 15000 N
Step 2:
Fc = (m * v^2) / r
Step 3:
mass = 15000 N / 9.8 m/s^2
Step 4:
v = (100 km/h) * (1000 m/km) / (3600 s/h)
Step 5:
Fc = (mass * v^2) / r
Step 6:
Ff = 0.9 * Fn
Substitute the values and calculate the results.
To find the frictional force acting on the tires when the car is traveling at 100 kph, we need to consider the forces acting on the car and apply the principles of circular motion.
First, let's calculate the speed of the car in meters per second (m/s) instead of kilometers per hour (kph). We can convert the speed from kph to m/s by dividing by 3.6:
Speed in m/s = (100 kph) / (3.6) ≈ 27.78 m/s
Given:
Mass of the car (m) = ??? (not given)
Weight of the car (W) = 15000 N
Radius of the curve (r) = 60 m
Banking angle (θ) = 30 degrees
Coefficient of friction (μ) = 0.90
Speed of the car (v) = 27.78 m/s
Now, we need to find the mass of the car (m) in order to determine the frictional force.
Since weight (W) is given, we can use the formula W = mg, where g is the acceleration due to gravity (approximately 9.8 m/s²) and solve for mass (m):
15000 N = m * 9.8 m/s²
m = 15000 N / 9.8 m/s²
m ≈ 1530.6 kg (rounded to three significant figures)
Now that we have the mass, we can proceed to calculate the frictional force (F_f) acting on the tires.
The frictional force (F_f) is given by the equation F_f = μ * N, where N is the normal force. The normal force can be calculated from the weight of the car and the banking angle.
Normal force (N) = W * cos(θ)
N = 15000 N * cos(30°)
N ≈ 12990 N (rounded to three significant figures)
Finally, we can calculate the frictional force (F_f):
F_f = μ * N
F_f = 0.90 * 12990 N
F_f ≈ 11,691 N (rounded to three significant figures)
Therefore, the frictional force acting on the tires when the car is traveling at 100 kph is approximately 11,691 N.