a race car travels 22 m/s around a circular track of radius 142 m/ what is magnitude of the resultant force on the 1400 kg driver answer his car? answer in units of kN. the angle from the wheel to the horizontal is 32 degree..and u= .11
To find the magnitude of the resultant force on the race car and the driver, we need to take into account the centripetal force and the force of friction.
First, let's calculate the centripetal force using the formula:
centripetal force = (mass * velocity^2) / radius
Given:
mass (m) = 1400 kg
velocity (v) = 22 m/s
radius (r) = 142 m
Plugging in these values, we get:
centripetal force = (1400 kg * (22 m/s)^2) / 142 m
centripetal force ≈ 4863.38 N
Next, let's calculate the force of friction using the formula:
force of friction = coefficient of friction * normal force
Given:
coefficient of friction (u) = 0.11
angle from the wheel to the horizontal (θ) = 32 degrees
First, let's calculate the normal force (N) using the formula:
normal force = mass * gravitational acceleration
Given:
gravitational acceleration (g) = 9.8 m/s^2
normal force = 1400 kg * 9.8 m/s^2
normal force ≈ 13720 N
Now, let's calculate the force of friction:
force of friction = 0.11 * 13720 N
force of friction ≈ 1509.2 N
Finally, to find the magnitude of the resultant force, we need to calculate the vector sum of the centripetal force and the force of friction. Since the angle between these forces is not given, we will assume they act at right angles to each other and use the Pythagorean theorem.
magnitude of resultant force = sqrt((centripetal force)^2 + (force of friction)^2)
magnitude of resultant force ≈ sqrt((4863.38 N)^2 + (1509.2 N)^2)
magnitude of resultant force ≈ sqrt(23670509.22 N^2 + 2277676.64 N^2)
magnitude of resultant force ≈ sqrt(25948185.86 N^2)
magnitude of resultant force ≈ 5093.36 N
Finally, to convert the magnitude of the resultant force to kilonewtons (kN), divide by 1000:
magnitude of resultant force ≈ 5093.36 N / 1000
magnitude of resultant force ≈ 5.09336 kN
Therefore, the magnitude of the resultant force on the 1400 kg driver and his car is approximately 5.09336 kN.