The coefficient of kinetic friction between a rubber tire and a dry concrete road is 0.700. What is the distance in which a car skid to a stop on such a road if its brakes are locked when it is moving at 60 km/h?
change speed to m/s
vf^2=vi^2+2 a d
where a= force/mass= g*mu
solve for distance d.
To find the distance in which a car will skid to a stop, we can use the equation:
d = (v^2) / (2 * μ * g)
Where:
d is the distance,
v is the initial velocity of the car,
μ is the coefficient of kinetic friction,
and g is the acceleration due to gravity (approximately 9.8 m/s^2).
First, we need to convert the velocity from km/h to m/s:
60 km/h * (1000 m/1 km) * (1 h/3600 s) = 16.67 m/s (rounded to two decimal places)
Now, we can substitute the values into the formula:
d = (16.67^2) / (2 * 0.700 * 9.8)
Let's calculate the distance:
d = (277.89) / (13.72)
d ≈ 20.24 meters (rounded to two decimal places)
Therefore, the car will skid to a stop in approximately 20.24 meters on the dry concrete road when its brakes are locked at a velocity of 60 km/h.
To find the distance a car will skid to a stop when its brakes are locked, we can use the equation:
distance = (velocity^2) / (2 * acceleration)
First, we need to find the acceleration of the car. The only force acting on the car after the brakes are locked is the force of kinetic friction. The formula for kinetic friction is:
force of kinetic friction = coefficient of kinetic friction * normal force
The normal force is the force exerted by the road on the car, which is equal to the weight of the car since the car is not accelerating vertically. Therefore,
force of kinetic friction = coefficient of kinetic friction * weight
The weight of the car is given by the formula:
weight = mass * gravity
where mass is the mass of the car and gravity is the acceleration due to gravity.
Now, let's put all the values into the formulas:
Given:
Coefficient of kinetic friction (µk) = 0.700
Velocity (v) = 60 km/h (We need to convert it to m/s)
Acceleration due to gravity (g) = 9.8 m/s^2
Step 1: Convert the velocity from km/h to m/s
1 km = 1000 m
1 hour = 3600 seconds
v = (60 km/h) * (1000 m / 1 km) * (1 h / 3600 s)
= 16.67 m/s
Step 2: Calculate the weight of the car
Assuming the mass of the car is given, we can calculate its weight.
For example, let's assume the mass of the car is 1000 kg.
weight = mass * gravity
= 1000 kg * 9.8 m/s^2
= 9800 N
Step 3: Calculate the force of kinetic friction
force of kinetic friction = coefficient of kinetic friction * weight
= 0.700 * 9800 N
= 6860 N
Step 4: Calculate the acceleration
Using Newton's second law, we know that force is equal to mass times acceleration (F = ma). In this case, the force is the force of kinetic friction, and the mass of the car cancels out, so:
force of kinetic friction = mass * acceleration
acceleration = force of kinetic friction / mass
= 6860 N / 1000 kg
= 6.86 m/s^2
Step 5: Calculate the distance
Using the equation, distance = (velocity^2) / (2 * acceleration), we substitute in the values:
distance = (16.67 m/s)^2 / (2 * 6.86 m/s^2)
= 4.896 m^2/s^2 / 13.72 m/s^2
= 0.3566 m
Therefore, the car will skid to a stop in approximately 0.3566 meters (or approximately 35.66 cm) on a dry concrete road with a coefficient of kinetic friction of 0.700 when its brakes are locked and it was initially moving at 60 km/h.