To find the coefficient of kinetic friction (μ), we can use the equation that relates the stopping distance (d), the mass of the object (m), and the coefficient of kinetic friction (μ):
d = (1/2) * μ * g * t^2
Where: d = Stopping distance (38 m) m = Mass of the object (248 kg) g = Acceleration due to gravity (9.8 m/s^2) t = Time taken to stop
To determine the time taken to stop, we can use the equation of motion:
d = u * t + (1/2) * a * t^2
Where: d = Stopping distance (38 m) u = Initial velocity (assuming it is zero, as the object comes to a stop) a = Acceleration
We know that the object comes to a stop, so its final velocity (v) is zero. Therefore, we can rearrange the equation as follows:
0 = u * t + (1/2) * a * t^2
Simplifying further: (1/2) * a * t^2 = -u * t
Since u is zero, the equation simplifies to: (1/2) * a * t^2 = 0
Since the object comes to a stop, we have a = 0. Therefore, the time taken to stop (t) is not defined using this equation. However, we can still determine the coefficient of kinetic friction (μ) using the first equation mentioned:
d = (1/2) * μ * g * t^2
Rearranging the equation to solve for μ: μ = (2 * d) / (g * t^2)
Although we don't have the exact time taken to stop, we can still calculate the coefficient of kinetic friction using the given values for stopping distance (d) and the mass of the object (m):
μ = (2 * 38 m) / (9.8 m/s^2 * t^2)
Without the value of t, we cannot determine the coefficient of kinetic friction accurately.