A 1500 kg automobile travels at a speed of 105 km/h along a straight concrete highway. Faced with an emergency situation, the driver jams on the brakes, and the car skids to a stop.
(a) What will be the car's stopping distance for dry pavement (µ = 0.85)?
(b) What will be the car's stopping distance for wet pavement (µ = 0.60)?
vf^2=vi^2+2 a d
but a=force/mass=-mu*mg/m=-mu*g
vf=0 change 105km/hr to m/s 29.16 ? check that.
0=29.16^2=mu*g*d
solve for d
To calculate the stopping distance of a car on dry or wet pavement, you need to use the following formula:
Stopping Distance = (Initial Velocity)^2 / (2 * (Coefficient of Friction) * (Acceleration due to Gravity))
(a) To calculate the stopping distance on dry pavement (µ = 0.85), plug the given values into the formula.
Initial velocity (v) is given as 105 km/h. To convert it to m/s, multiply by 1000/3600:
v = 105 km/h * (1000 m/3600 s) = 29.2 m/s
The coefficient of friction (µ) for dry pavement is given as 0.85.
Acceleration due to gravity (g) is approximately 9.8 m/s^2.
Plug these values into the formula to find the stopping distance:
Stopping Distance = (29.2 m/s)^2 / (2 * 0.85 * 9.8 m/s^2) = 44.75 meters
Therefore, the car's stopping distance on dry pavement is approximately 44.75 meters.
(b) To calculate the stopping distance on wet pavement (µ = 0.60), repeat the same steps as in part (a) but using the new coefficient of friction.
The coefficient of friction (µ) for wet pavement is given as 0.60.
Plug these values into the formula to find the stopping distance:
Stopping Distance = (29.2 m/s)^2 / (2 * 0.60 * 9.8 m/s^2) = 61.42 meters
Therefore, the car's stopping distance on wet pavement is approximately 61.42 meters.