A car is traveling at 54.2 km/h on a flat highway. The acceleration of gravity is 9.81 m/s^2.

Question

A car is traveling at 54.2 km/h on a flat highway. The acceleration of gravity is 9.81 m/s^2.

PART 1: If the coefficient of kinetic friction between the road and the tires on a rainy day is 0.131, what is the minimum distance needed for the car to stop? Answer in unitsof m.
PART 2: What is the stopping distance when the surface is dry and the coefficient of kinetic friction is 0.603? Answer in units of m.

Answer 1

Frictional resistance, F

= -μ mg
acceleration, a
= F/m
= -μg

For distance S, use
v²-u²=2aS
where v=final velocity =0
u=initial velocity = 54.2 km/h = 15.06 m/s
Solve for S.

1. μ=0.131
u=54.2
a=-0.131*9.8=-1.284 m/s²
S=15.06²/(-2*1.284)
=88.3m

The same approach can be used for both cases.

Post your answers for a check if you wish.

Answer 2

omg thx so much!!!!

Answer 3

To find the minimum stopping distance, we need to calculate the force of kinetic friction acting on the car.

PART 1:
Given:
Initial velocity (v0) = 54.2 km/h = 15.06 m/s
Acceleration due to gravity (g) = 9.81 m/s^2
Coefficient of kinetic friction (μ) = 0.131

First, we find the force of kinetic friction using the formula:

F_kinetic = μ * m * g

Since the mass of the car cancels out in this calculation, it is not necessary to know the mass of the car.

F_kinetic = 0.131 * g

Next, we can calculate the deceleration:

a = F_kinetic / m

Since we know the mass cancels out, the deceleration a is:

a = F_kinetic

Now, we can find the stopping distance (d) using the following formula:

v^2 = v0^2 + 2 * a * d

Rearranging the formula, we have:

d = (v^2 - v0^2) / (2 * a)

Let's plug in the values and calculate:

d = (0^2 - 15.06^2) / (2 * -0.131 * 9.81)
d = -15.06^2 / (-2 * 0.131 * 9.81)
d = 112.85 m

Therefore, the minimum distance needed for the car to stop on a rainy day is approximately 112.85 meters.

PART 2:
Given:
Coefficient of kinetic friction (μ) = 0.603

Using the same formulas as before, we can calculate the stopping distance for the dry surface where μ = 0.603.

F_kinetic = 0.603 * g

The deceleration a = F_kinetic = 0.603 * g

d = (0^2 - 15.06^2) / (2 * -0.603 * 9.81)
d = 112.85 m

Therefore, the stopping distance on a dry surface with a coefficient of kinetic friction of 0.603 is also approximately 112.85 meters.

Answer 4

To find the stopping distance of the car, we need to consider the forces acting on it and use the equations of motion. Let's analyze each part separately.

PART 1:
In this case, the coefficient of kinetic friction is given as 0.131. The force of friction can be calculated using the equation:
Force of friction = coefficient of kinetic friction * Normal force

The normal force is equal to the weight of the car, which can be found using the equation:
Weight = mass * acceleration due to gravity

Given that the acceleration due to gravity is 9.81 m/s^2, we can use this to find the normal force. However, we need to convert the car's velocity from km/h to m/s, as the remaining calculations will be done in SI units.

Converting the car's velocity:
54.2 km/h * (1000 m/1 km) * (1 h / 3600 s) = 15.06 m/s

Now, let's calculate the normal force:
Weight = mass * acceleration due to gravity
The mass of the car is not given, but we don't need it because it cancels out in the subsequent equations.

Next, we need to calculate the deceleration due to friction. The equation for deceleration is given by:
Deceleration = (Force of friction) / (mass)

Since the mass cancels out, we only need to calculate the force of friction.

Force of friction = coefficient of kinetic friction * Normal force

Substituting the values:
Force of friction = 0.131 * (Weight)
Deceleration = (Force of friction) / (mass)

Finally, we can calculate the minimum stopping distance using the equation:
Stopping distance = (Initial velocity^2) / (2 * deceleration)

Substituting the values and solving for Stopping distance:
Stopping distance = (Initial velocity^2) / (2 * deceleration)

PART 2:
In this case, the coefficient of kinetic friction is given as 0.603. We can follow the same steps as in Part 1, but with a different coefficient of friction.

First, convert the car's velocity from km/h to m/s as before.

Then, calculate the normal force and the deceleration due to friction using the equations mentioned earlier.

Lastly, substitute the values into the stopping distance equation and solve for stopping distance.

Now that you have the step-by-step explanation, you can apply these calculations to find the stopping distances for both scenarios.