A 2000kg car traveling at a speed of 27m/s skids to a halt on wet concrete where μk = 0.20.
M*g = 2000kg * 9.8N./kg = 19,600 N. = Wt
of car. = Normal Force(Fn).
a = u*g = 0.2 * (-9.8) = -1.96 m/s^2.
d = -Vo^2/2a = -(27^2)/-3.92 = 186 m. =
Stopping distance.
To find the stopping distance of the car on wet concrete, we can use the concept of kinetic friction.
Step 1: Convert the speed from m/s to km/h (optional)
Since the coefficient of kinetic friction (μk) is unitless, we can choose to keep the speed in m/s or convert it to km/h for convenience. Let's convert to km/h:
Speed in km/h = speed in m/s × (3.6 km/h)/(1 m/s)
Speed in km/h = 27 m/s × (3.6 km/h)/(1 m/s)
Speed in km/h = 97.2 km/h
Step 2: Calculate the force of kinetic friction (Fk)
The force of kinetic friction can be determined using the formula:
Fk = μk × N
where μk is the coefficient of kinetic friction and N is the normal force.
Step 3: Calculate the normal force (N)
The normal force acting on the car can be determined using the formula:
N = m × g
where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).
N = 2000 kg × 9.8 m/s^2
N = 19600 N
Step 4: Calculate the force of kinetic friction (Fk)
Fk = μk × N
Fk = 0.20 × 19600 N
Fk = 3920 N
Step 5: Calculate the deceleration (a) of the car
The deceleration of the car can be determined using Newton's second law of motion:
F = m × a
where F is the net force and m is the mass of the car.
To calculate the net force, we can use:
F = Fk
Fk = m × a
3920 N = 2000 kg × a
a = 1.96 m/s^2
Step 6: Calculate the stopping distance (d)
The stopping distance can be calculated using the formula:
d = (v^2) / (2a)
where v is the initial velocity and a is the deceleration.
d = (27 m/s)^2 / (2 × 1.96 m/s^2)
d = 729 m^2/s^2 / (3.92 m/s^2)
d = 186.07 m
Therefore, the car will skid to a halt on wet concrete with a stopping distance of approximately 186 meters.
To determine the stopping distance of the car on wet concrete, we can use the equation of motion:
v² = u² + 2as
Where:
v = final velocity (0 m/s since the car comes to a halt)
u = initial velocity (27 m/s)
a = acceleration
s = stopping distance
First, let's find the acceleration using the formula:
a = (v² - u²) / (2s)
Given that v = 0 m/s and u = 27 m/s, we have:
a = (0² - 27²) / (2s)
a = (-729) / (2s)
a = -364.5 / s
The negative sign indicates that the acceleration acts in the opposite direction of the initial velocity, i.e., slowing down the car.
Now, we need to determine the coefficient of kinetic friction (μk). The equation for frictional force is:
F = μk * N
Where:
F = frictional force
μk = coefficient of kinetic friction
N = normal force
Since the car skids to a halt, the frictional force opposes the motion and causes the deceleration. The normal force is equal to the weight of the car which is given by:
N = m * g
Where:
m = mass of the car (2000 kg)
g = acceleration due to gravity (9.8 m/s²)
N = 2000 * 9.8 = 19600 N
Now we can calculate the frictional force:
F = μk * N
F = 0.20 * 19600
F = 3920 N
The frictional force is equal to the mass of the car multiplied by the acceleration:
F = m * a
3920 = 2000 * a
a = 3920 / 2000
a = 1.96 m/s²
Now we can solve for the stopping distance (s) using the equation:
a = -364.5 / s
1.96 = -364.5 / s
To solve for s, we can rearrange the equation:
s = -364.5 / 1.96
s ≈ -186.07 m
Since distance cannot be negative, we take the magnitude of the stopping distance:
s ≈ 186.07 m
Therefore, the car skids to a halt on wet concrete with a stopping distance of approximately 186.07 meters.