According to test performed by the manufactures, an automobile with an initial speed of 75 km/h has a stopping distance of 25 m on a level road. assuming that no skidding occurs during breaking, what is the value of μ , between the wheels and the road required to achieve the stopping distance?
Well, if you're looking for the value of μ, I have to admit it's a bit slippery... just like my sense of humor! But fear not, I'll do my best to provide a somewhat helpful answer.
To find the value of μ, we can use the equation for stopping distance, which is given by:
stopping distance = (initial velocity²) / (2 * μ * gravitational acceleration)
Given that the stopping distance is 25 m and the initial velocity is 75 km/h (which needs to be converted to m/s), we can rearrange the equation to solve for μ:
μ = (initial velocity²) / (2 * gravitational acceleration * stopping distance)
First, let's convert the initial velocity from km/h to m/s:
75 km/h * (1000 m/1 km) * (1/3600 h/1 s) = 20.83 m/s (approximately)
Now, let's plug in the values into the formula:
μ = (20.83 m/s)² / (2 * 9.8 m/s² * 25 m)
μ ≈ 0.172
So, the value of μ, between the wheels and the road required to achieve the stopping distance of 25 m, is approximately 0.172. But remember, this is just an approximation, so don't go skidding around with it!
To determine the value of μ (coefficient of friction) between the wheels and the road required to achieve the stopping distance, we can use the equation for stopping distance:
Stopping Distance = (initial velocity^2) / (2 * acceleration)
Since the acceleration is the result of friction, we can express it as:
Acceleration = μ * g
Where:
μ = coefficient of friction
g = acceleration due to gravity (~9.8 m/s^2)
Given that the stopping distance is 25 m and the initial velocity is 75 km/h, we need to convert the initial velocity to m/s:
75 km/h = 75 * (1000 m / 1 km) / (3600 s / 1 h) = 20.83 m/s
Now, we can rearrange the equation and solve for μ:
25 = (20.83^2) / (2 * μ * 9.8)
25 = 433.889 / (19.6 * μ)
25 * 19.6 * μ = 433.889
μ = 433.889 / (25 * 19.6)
μ ≈ 0.88
Therefore, the value of μ (coefficient of friction) required to achieve the stopping distance is approximately 0.88.
To find the value of μ (the coefficient of friction) required to achieve the stopping distance of 25 m, we can use the following formula:
stopping distance = (initial velocity^2) / (2 * acceleration)
Here, the initial velocity is given as 75 km/h, which needs to be converted into m/s. The acceleration can be calculated using the formula:
acceleration = μ * g
where g is the acceleration due to gravity, approximately 9.8 m/s².
First, let's convert the initial velocity from km/h to m/s:
75 km/h = (75 * 1000) / 3600 m/s
= 20.83 m/s (rounded to two decimal places)
Now, we can substitute the values into the formula for the stopping distance:
25 = (20.83^2) / (2 * μ * 9.8)
To find the value of μ, we can rearrange the formula and solve for it. Let's multiply both sides of the equation by 2 * μ * 9.8:
50 * μ * 9.8 * 25 = 20.83^2
Next, divide both sides of the equation by (20.83^2):
μ = (20.83^2) / (50 * 9.8 * 25)
Calculating this expression will provide the value of μ required to achieve the given stopping distance.