A car moving at 60 km/h skids 13 m with locked brakes. How far will the car skid with locked brakes at 180 km/h?
Convert initial velocities to m/s
60 km/h=60*1000/3600 m/s=16.67 m/s
180 km/h = 50 m/s
Use kinematic equation:
v^2-u^2=2aS
where
u=initial velocity
v=final velocity
a=acceleration (deceleration is negative)
S=distance travelled before stopping
To determine how far the car will skid with locked brakes at 180 km/h, we can use the concept of the coefficient of friction and the equation for stopping distance.
The stopping distance of a vehicle depends on multiple factors, such as the coefficient of friction between the tires and the road, the initial velocity of the car, and the time it takes for the car to come to a complete stop.
In this case, we are assuming locked brakes, which means the tires are skidding and the coefficient of friction is constant. Therefore, we can assume that the coefficient of friction remains the same for both speeds.
The equation for stopping distance is:
Stopping Distance = (Initial Velocity²) / (2 * Coefficient of Friction * Acceleration due to Gravity)
Given that the initial velocity is changing from 60 km/h to 180 km/h, we need to convert these velocities to meters per second (m/s) to be consistent with the units used in the equation.
1 km/h = 1000 m / 3600 s = 10/36 m/s
So, the initial velocity for the car moving at 60 km/h is:
60 km/h * (10/36) m/s = 16.67 m/s
And the initial velocity for the car moving at 180 km/h is:
180 km/h * (10/36) m/s = 50 m/s
As mentioned earlier, the coefficient of friction remains the same in this scenario.
Now, we can calculate the stopping distances for the two scenarios.
For the car moving at 60 km/h:
Stopping Distance = (16.67 m/s)² / (2 * Coefficient of Friction * Acceleration due to Gravity)
And for the car moving at 180 km/h:
Stopping Distance = (50 m/s)² / (2 * Coefficient of Friction * Acceleration due to Gravity)
Given that the stopping distance for the car moving at 60 km/h is given as 13 m, we can use this information to determine the coefficient of friction.
13 m = (16.67 m/s)² / (2 * Coefficient of Friction * Acceleration due to Gravity)
Simplifying the equation, we have:
Coefficient of Friction = (16.67 m/s)² / (2 * 13 m * Acceleration due to Gravity)
Now, we can substitute this value of the coefficient of friction back into the equation for the car moving at 180 km/h:
Stopping Distance = (50 m/s)² / (2 * Coefficient of Friction * Acceleration due to Gravity)
Substituting the value of the coefficient of friction we calculated earlier into this equation, we can solve it to find the stopping distance.
Please note that the value of the coefficient of friction might not be accurately determined without additional information or experimentation. The above calculations assume a constant coefficient of friction for simplicity.