Jason approaches a rotary in her 3,500kg Mercedes. Its radius of curvature 95m but his speed is 25m/s. The acceleration is 6.6 m/s^2. What is the coefficient friction between his tires and the road?
I know Mu mg=mv^2/R but I am unable to complete my equation and continue to end up with a negative number
Netative number?
mu=v^2/(Rg) R=95, g= 9.8, v^2=positive.
How are you getting a negative number? mu is defined as friction force divided by force normal. don't use -9.8m/s^2 times mass as force normal. Forces have directions, that can change - to +
ok I think I figured it out mu=0.67
thank you for your help
To find the coefficient of friction between the tires and the road, we can use the equation:
μmg = mv^2/R
where:
μ is the coefficient of friction,
m is the mass of the Mercedes (3,500 kg),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
v is the velocity of the Mercedes (25 m/s), and
R is the radius of curvature (95 m).
Substituting the given values into the equation, we have:
μ * 3,500 kg * 9.8 m/s^2 = 3,500 kg * (25 m/s)^2 / 95 m
Simplifying further, we get:
μ * 34,300 N = 9,625 kg * m^2/s^2 / 95 m
Now, we can rearrange the equation to solve for μ:
μ = (9,625 kg * m^2/s^2 / 95 m) / 34,300 N
μ = 0.2806
Therefore, the coefficient of friction μ between the tires and the road is approximately 0.2806.
If you were getting negative numbers in your calculation, it might be due to a sign error or mistake in the calculation. Please double-check the values and ensure the correct units are used throughout the calculation.