Drag race tires in contact with an asphalt surface probably have one of the higher coefficients of static friction in the everyday world. Assuming a constant acceleration and no slipping of tires estimate the coefficient of static friction for a drag racer that covers the quarter mile in 6.0s
To estimate the coefficient of static friction for a drag racer, we can use the following equation:
a = (v_f - v_i) / t
Where:
- a is the acceleration of the drag racer,
- v_f is the final velocity of the drag racer,
- v_i is the initial velocity of the drag racer, and
- t is the time taken to cover the quarter mile.
Assuming a constant acceleration and no slipping of the tires, the acceleration (a) can be calculated as:
a = 2 * s / t^2
Where:
- s is the distance covered by the drag racer, which is one-quarter mile or approximately 402.34 meters.
Hence, the formula becomes:
2 * s / t^2 = (v_f - v_i) / t
Since the drag racer likely starts from rest (v_i = 0), the equation simplifies to:
2 * s / t^2 = v_f / t
Now, let's rearrange the equation to solve for the coefficient of static friction.
First, we need to find v_f (final velocity) by rearranging the well-known equation:
v_f = v_i + a * t
Since v_i = 0, the equation simplifies to:
v_f = a * t
Now, substitute v_f = a * t back into the equation:
2 * s / t^2 = (a * t) / t
Simplifying further:
2 * s / t^2 = a
Finally, we can solve for the coefficient of static friction (μ) by rearranging the equation:
μ = a / g
Where:
- g is the acceleration due to gravity, approximately 9.8 m/s^2.
By substituting the previously calculated acceleration (a) into the equation, we can find the coefficient of static friction (μ).
To estimate the coefficient of static friction for a drag racer, we need to rearrange the formula for acceleration to solve for the coefficient of friction. The formula for acceleration is:
acceleration = (final velocity - initial velocity) / time
Given:
- Time (t) = 6.0 seconds
- Distance covered (d) = quarter mile = 402.34 meters
- Initial velocity (u) = 0 m/s (assuming the drag racer starts from rest)
Since the drag racer covers a quarter mile in 6.0 seconds and we assume constant acceleration, we can use the formula for distance:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Rearranging the formula for acceleration, we get:
acceleration = (2 * (distance - initial velocity * time)) / time^2
Substituting the values into the formula:
acceleration = (2 * (402.34 - 0 * 6.0)) / (6.0^2)
acceleration = (2 * 402.34) / 36
acceleration = 8.897 m/s^2
Now, using the formula for static friction:
static friction = coefficient of friction * normal force
The normal force is equal to the weight of the drag racer because there is no vertical motion. However, since we only need to estimate the coefficient of static friction, we can ignore the actual weight of the drag racer.
Therefore, the formula becomes:
static friction = coefficient of friction * weight (we can assume weight = 1)
To calculate the static friction, we need to determine the weight of the drag racer. However, since we are estimating the coefficient of static friction, we can assume the weight of the drag racer is 1 unit (e.g., 1 kg).
Therefore, the static friction is equal to the acceleration:
static friction = 8.897 N
Finally, substituting the values into the formula, we get:
8.897 N = coefficient of friction * 1
Therefore, the coefficient of static friction for the drag racer is approximately 8.897. Note that this is just an estimate and may vary in actual conditions.
f = m a
μ m g = m (d / t²)
μ = (d / t²) / g = (1320 / 6²) / 32
the assumption is that all of the mass acts on the driving wheels