You are traveling in your car at a velocity of 24.0m/s east when you slam on your brakes. The
force of friction on your car tires is 1.80x10
4N. IF the mass of you and your car is 1.50x103
kg,
how far do you skid before stopping?
F = ma, so a = 1.8*10^4 / 1.50*10^3 = 12 m/s^2
v^2 = 2as, so
24^2 = 2*12*s
s = 24 m
Well, that sounds like quite the adventure! Let me calculate that for you.
So we know the force of friction is 1.80x10^4 N and the mass is 1.50x10^3 kg. To find the distance you skid before stopping, we can use the equation:
Friction force = mass x acceleration
Rearranging the equation, we have:
Acceleration = Friction force / mass
Plugging in the values, we get:
Acceleration = (1.80x10^4 N) / (1.50x10^3 kg)
Now, let me grab my calculator... (beep boop beep boop) ...
The acceleration is 12 m/s^2.
To find the distance, we can use the equation:
Distance = (initial velocity^2) / (2 x acceleration)
Since your initial velocity is 24.0 m/s, we have:
Distance = (24.0 m/s)^2 / (2 x 12 m/s^2)
Calculating again... (beep boop beep boop) ...
You will skid for approximately 24.0 meters before stopping. So, hold on tight, and enjoy the skid!
To find the distance you skid before stopping, you can use the equations of motion. First, we need to find the deceleration of the car using Newton's second law of motion:
Force = mass x acceleration
Rearranging the equation, we get:
Acceleration = Force / mass
Acceleration = (1.80x10^4 N) / (1.50x10^3 kg)
Acceleration = 12.0 m/s^2 (rounded to one decimal place)
Next, we can use the equations of motion to find the distance:
vf^2 = vi^2 + 2ad
In this case, the initial velocity (vi) is 24.0 m/s (since the car is moving east) and the final velocity (vf) is 0 (since the car comes to a stop). The acceleration (a) is -12.0 m/s^2 (negative because it opposes the initial motion). We need to solve for the distance (d).
0 = (24.0 m/s)^2 + 2(-12.0 m/s^2)d
0 = 576 m^2/s^2 - 24 m/s^2d
24 m/s^2d = 576 m^2/s^2
d = 576 m^2/s^2 / 24 m/s^2
d = 24.0 m
Therefore, you skid a distance of 24.0 meters before stopping.
To find the distance you skid before stopping, you need to use the equations of motion. The key equation you'll use is:
v^2 = u^2 + 2as
Where:
v = final velocity (which is 0 since you come to a stop)
u = initial velocity (24.0 m/s east)
a = acceleration (caused by the force of friction)
s = distance
First, let's calculate the acceleration (a) using Newton's second law:
F = ma
Rearranging the equation, we have:
a = F/m
Substituting the given values, we get:
a = (1.80x10^4 N) / (1.50x10^3 kg)
= 12.0 m/s^2
Now, plug the values of u, a, and v into the equation of motion:
0^2 = (24.0 m/s)^2 + 2(12.0 m/s^2)s
Simplifying the equation gives us:
0 = 576.0 m^2/s^2 + 24.0 m/s^2 s
Rearranging and isolating the s term, we get:
s = -576.0 m^2/s^2 / (24.0 m/s^2)
= -24.0 m
Since distance cannot be negative, we take the absolute value:
s = 24.0 m
Therefore, you skid 24.0 meters before stopping.