please help...i need this immediately..
rolling friction. two bicycles are set rolling with the same initial speed of 3.50m/s on a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40psi and goes 18.1m; the other is at 105 psi and goes 92.9m. what is the coefficient ...of rolling friction µr for each? Assume that the net horizontal force is due to rolling friction only.
You don't need to use the tire pressures to compute µr -- you just need the rolling distance, X.
Use a conservation of energy approach. Set 3/4 of the initial kinetic energy equal to the work done against rolling friction. The "3/4" is the fraction of KE lost while the bike reaches half the initial speed
(1/2)*(3/4)*M*V^2 = M*g*µr*X
µr = (3/8)*V^2/(gX)
Use that formula for both bicycles.
qwe
To find the coefficient of rolling friction, we can use the formula:
μr = (2g * d) / (v^2)
Where:
μr is the coefficient of rolling friction,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
d is the distance traveled before the speed is reduced by half, and
v is the initial speed.
Let's calculate the coefficient of rolling friction for each bicycle tire:
For the tire inflated to 40 psi:
Given:
Initial speed, v = 3.50 m/s
Distance traveled before speed reduced by half, d = 18.1 m
Using the formula:
μr = (2 * 9.8 m/s^2 * 18.1 m) / (3.50 m/s)^2
Calculating further:
μr = 2 * 9.8 m/s^2 * 18.1 m / 12.25 m^2/s^2
Simplifying the equation:
μr = 35.56 / 12.25
μr ≈ 2.90
Therefore, the coefficient of rolling friction for the tire inflated to 40 psi is approximately 2.90.
Now, let's calculate the coefficient of rolling friction for the tire inflated to 105 psi:
Given:
Initial speed, v = 3.50 m/s
Distance traveled before speed reduced by half, d = 92.9 m
Using the formula:
μr = (2 * 9.8 m/s^2 * 92.9 m) / (3.50 m/s)^2
Calculating further:
μr = 2 * 9.8 m/s^2 * 92.9 m / 12.25 m^2/s^2
Simplifying the equation:
μr = 181.52 / 12.25
μr ≈ 14.83
Therefore, the coefficient of rolling friction for the tire inflated to 105 psi is approximately 14.83.