If the retardation produced due to braking is 3.1 m/s2, the braking efficiency is
31%
Calculating Braking Efficiency
Braking efficiency is a measure of how effective a vehicle's braking system is. It is often expressed as a percentage and relates the actual deceleration (retardation) achieved to the maximum possible deceleration.
The maximum theoretical deceleration possible for a vehicle is limited by the friction between the tires and the road surface. Under ideal conditions, this maximum deceleration is approximately equal to the acceleration due to gravity, denoted by \(g\).
The formula used to calculate braking efficiency is:
\[ \text{Braking Efficiency} = \left( \frac{\text{Achieved Retardation}}{\text{Acceleration due to Gravity}} \right) \times 100\% \]Given Information
- Retardation produced due to braking = \(3.1 \, m/s^2\)
Assumed Value for Acceleration due to Gravity
We will use the standard approximate value for the acceleration due to gravity:
- Acceleration due to Gravity (\(g\)) \( \approx 9.8 \, m/s^2 \)
Step-by-Step Calculation
Now, we can plug the given values into the formula to calculate the braking efficiency:
\[ \text{Braking Efficiency} = \left( \frac{3.1 \, m/s^2}{9.8 \, m/s^2} \right) \times 100\% \] \[ \text{Braking Efficiency} = \left( \frac{3.1}{9.8} \right) \times 100\% \] \[ \text{Braking Efficiency} \approx 0.3163 \times 100\% \] \[ \text{Braking Efficiency} \approx 31.63\% \]Comparing with Options
The calculated braking efficiency is approximately 31.63%. Let's compare this value with the given options:
- Option 1: 20%
- Option 2: 31%
- Option 3: 25%
- Option 4: 35%
The calculated value of 31.63% is closest to 31%. Therefore, the braking efficiency is approximately 31%.
This calculation demonstrates how the braking efficiency relates the actual stopping capability (retardation) to the force of gravity limiting the maximum possible deceleration.
Important Questions from Kinematics and Kinetics
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A body of mass 10 kg moving with a velocity of 1 m/s is acted upon by a force of 50 N for two seconds. The final velocity will be:
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Each of four particles move along an x-axis. Their coordinates (in meters) as functions of time (in seconds) are given by
1) particle 1: x (t) = 3.5 – 2.7 t3
2) particle 2: x (t) = 3.5 + 2.7 t3
3) particle 3: x (t) = 3.5 – 2.7 t2
4) particle 4: x (t) = 3.5 – 3.4t - 2.7 t2
Which of these particles have constant acceleration?
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