A braking system is used to prevent the car travelling
faster than 27 m s–1.The car and passengers shown in the diagram have a total mass of 750 kg. The length of track from P to Q is 80 m. Calculate the average braking force that would be required if the speed of the car is to be limited to 27 m s–1.
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To calculate the average braking force required to limit the speed of the car to 27 m/s, we can use the following equation:
Force = Mass * Acceleration
To find the acceleration, we can use the equation:
Acceleration = Change in Velocity / Time Taken
Since the initial velocity is not given, we can assume it to be zero.
Change in Velocity = Final Velocity - Initial Velocity
= 27 m/s - 0 m/s
= 27 m/s
Time Taken = Distance / Velocity
= 80 m / 27 m/s
= 2.963 s
Acceleration = Change in Velocity / Time Taken
= 27 m/s / 2.963 s
= 9.119 m/s^2
Now we can calculate the average braking force using the formula
Force = Mass * Acceleration
= 750 kg * 9.119 m/s^2
= 6,839.25 N (rounded to 2 decimal places)
Therefore, the average braking force required to limit the speed of the car to 27 m/s is approximately 6,839.25 N.
To calculate the average braking force required to limit the speed of the car to 27 m/s, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):
F = m * a
In this case, the acceleration will be negative since the car is decelerating to come to a stop. The acceleration can be calculated using the kinematic equation:
v^2 = u^2 + 2a * s
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
In this case, the initial velocity (u) is the speed of the car before braking, which we'll assume is 0 m/s since it's not given. The final velocity (v) is 27 m/s, and the distance (s) is 80 m.
Substituting these values into the equation:
27^2 = 0^2 + 2a * 80
729 = 160a
Now we can solve for the acceleration:
a = 729 / 160
a ≈ 4.55625 m/s^2
Now that we have the acceleration, we can calculate the average braking force using Newton's second law:
F = m * a
Given that the total mass (m) of the car and passengers is 750 kg:
F = 750 kg * 4.55625 m/s^2
F ≈ 3417.19 N
Therefore, the average braking force required to limit the car's speed to 27 m/s is approximately 3417.19 N.