Find the minimum stopping distance for a car moving at 108km/h if the coefficient of static friction between the tires and road is 0.9
I really don't understand pls helppp
108,000m/hr * 1hr/3600s = 30 m/s
friction force= -.9 m g
= -.9 * 9.81 m = -8.83 m
F = m a
-8.83 m = m a
a = -8.83 m/s^2
v = Vi + a t
0 = 30 - 8.83 t
t = 4 seconds
To find the minimum stopping distance for a car moving at 108 km/h with a given coefficient of static friction between the tires and the road, we need to use the equations of motion and the concept of kinetic friction.
The key equation we'll use is the equation that relates the stopping distance (d), initial velocity (v₀), coefficient of friction (μ), and acceleration due to gravity (g):
d = (v₀²) / (2μg)
Here's how to calculate the minimum stopping distance:
Step 1: Convert the initial velocity from km/h to m/s.
To convert km/h to m/s, use the conversion factor of 1 km/h = 0.27778 m/s. Thus, the initial velocity (v₀) in m/s will be:
v₀ = 108 km/h * (0.27778 m/s/km/h)
v₀ = 30 m/s (approximately)
Step 2: Determine the acceleration due to gravity (g).
The acceleration due to gravity is approximately 9.8 m/s².
Step 3: Calculate the minimum stopping distance (d).
Using the formula d = (v₀²) / (2μg), plug in the values:
d = (30 m/s)² / (2 * 0.9 * 9.8 m/s²)
d = 900 / (17.64)
d ≈ 51.02 m (approximately)
Therefore, the minimum stopping distance for the car moving at 108 km/h with a coefficient of static friction of 0.9 is approximately 51.02 meters.