Drag-race tires in contact with an asphalt surface have a very high coefficient of static fric.tion. Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 2.1 km in 8 s, starting from rest.
Coefficient of static friction =
d = (1/2) a t^2
solve for a
F = m a = mu m g
so
mu = a/g
d=ut+1/2at² , u=0
2100=(0)t+1/2a(8)²
a=65.63m/s²
Fx=ma
Ffr=ma.{1}
Fy=ma , Fy= Fn-mg , Fy=0
Fn=mg.{2}
Ffr=µsFn
ma=µs(mg)
a/g=µs
65.63/9.8=µs
µs=6.70N
Well, if we're talking about drag racing, I hope those tires have a good sense of style too! Let's calculate that coefficient of static friction for you.
To calculate the coefficient of static friction, we can use the equation:
distance = (initial velocity * time) + (1/2 * acceleration * time^2)
Since the car starts from rest, the initial velocity is 0. We can rearrange the equation to solve for acceleration:
acceleration = (2 * distance) / (time^2)
Plugging in the values, we get:
acceleration = (2 * 2.1 km) / (8 s)^2
Let's convert the distance to meters and the time to seconds for consistent units:
acceleration = (2 * 2100 m) / (8 s)^2
Simplifying further:
acceleration = 525 m / 64 s^2
Now, we know that the acceleration is equal to the coefficient of static friction multiplied by the acceleration due to gravity (9.8 m/s^2). So we can write:
coefficient of static friction = acceleration / (9.8 m/s^2)
Plugging in the values:
coefficient of static friction = (525 m / 64 s^2) / (9.8 m/s^2)
Calculating that, we get:
coefficient of static friction ≈ 0.855
So, the drag racer would need a coefficient of static friction of approximately 0.855 to cover 2.1 km in 8 seconds, starting from rest. That's quite a grip!
To estimate the coefficient of static friction needed for the drag racer to cover a distance of 2.1 km in 8 seconds, we can use the kinematic equations of motion.
The kinematic equation used for this scenario is:
d = v_i * t + 0.5 * a * t^2
where:
d is the distance covered (2.1 km or 2100 m),
v_i is the initial velocity (0 m/s since the car starts from rest),
t is the time taken (8 seconds),
a is the acceleration (which we need to find), and
t^2 represents time squared.
Rearranging the equation, we have:
a = (2 * (d - v_i * t)) / t^2
Substituting the known values, we have:
a = (2 * (2100 - 0 * 8)) / (8^2)
= (2 * 2100) / 64
= 65.625 m/s^2
Now, the coefficient of static friction (μ_s) can be determined using the following equation:
a = μ_s * g
where:
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Rearranging the equation, we have:
μ_s = a / g
Substituting the values, we get:
μ_s = 65.625 / 9.8
≈ 6.69
Therefore, the coefficient of static friction needed for the drag racer to cover 2.1 km in 8 seconds, starting from rest, is approximately 6.69.