Calculating the Stopping distance

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SUMMARY

The discussion focuses on calculating the stopping distance of a car with a mass of 1000 kg traveling at 100 km/hr, considering a coefficient of friction (μ) of 0.8. The propulsive power delivered by the engine while cruising at 120 km/hr is calculated to be 15 kW using the formula P = F * v, where F is the drag force of 450 N and v is the velocity in m/s. The stopping distance can be determined using the equation D = V² / (2 * μ * g), where g is the acceleration due to gravity (9.8 m/s²), and mass is not required for this calculation.

PREREQUISITES
  • Understanding of basic physics concepts such as force, mass, and acceleration.
  • Familiarity with the equations of motion and energy, particularly in the context of vehicles.
  • Knowledge of the coefficient of friction and its role in braking calculations.
  • Ability to convert units, specifically from km/hr to m/s.
NEXT STEPS
  • Study the derivation and application of the equation D = V² / (2 * μ * g) for stopping distance calculations.
  • Learn about the principles of momentum conservation and the coefficient of restitution in collision scenarios.
  • Explore the relationship between power, force, and velocity in automotive engineering.
  • Investigate the effects of different coefficients of friction on braking distances in various conditions.
USEFUL FOR

This discussion is beneficial for physics students, automotive engineers, and anyone involved in vehicle dynamics and safety analysis, particularly in understanding braking performance and collision outcomes.

xavierengineering
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Homework Statement


A car of mass 1000 kg is cruising at 120 km/hr. At this velocity the drag and friction forces that the engine needs to work against is equivalent to 450 N.

(i) What is the propulsive power being delivered by the engine when cruising? (4 marks)

(ii) From a velocity of 100 km/hr, the driver suddenly sees a traffic jam ahead and performs an emergency braking, resulting in locking the four wheels. Calculate the minimum braking distance required to bring the car to a full stop.

Assume the following: The coefficient of friction between the tyres and road is μ = 0.8.
Consider the weight of the vehicle to be equally distributed on each wheel while braking The drag or other friction forces are not significant in this case. g = 9.8 m/s2

Homework Equations


D=V/2*0.8*9.81

The Attempt at a Solution


All i know for the equation is D=V/2*0.8*9.81. However i am not sure how to implement the mass into the equation, Or if there is a different one to use.
 
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The equation you quote is fine for part two. Why do you wish to bring mass into it?
For part one, you need some more standard equations. What ones do you know about power, force, mass, acceleration?
 
I worked out Q 1 = 15KW
By using the P= 450*(120/3.6)=15KW

But for part be i assumed the weight must be added to the equation because it states the mass of the car. Or is that figure irrelevant to work out the distance ?
 
I also forgot to add this to the question..
The driver cannot avoid hitting the vehicle at the back of the queue. At the moment of impact, the driver's car has a remaining velocity of 15 km/hr and hits a stationary van that has a mass 1400 kg.
Assume that both vehicles are in neutral and not braking at the moment of impact. Neglect the effects of friction.

Calculate the velocities of each vehicle after impact if the coefficient of restitution of the vehicles' bumpers is 0.85.
 
xavierengineering said:
I also forgot to add this to the question..
The driver cannot avoid hitting the vehicle at the back of the queue. At the moment of impact, the driver's car has a remaining velocity of 15 km/hr and hits a stationary van that has a mass 1400 kg.
Assume that both vehicles are in neutral and not braking at the moment of impact. Neglect the effects of friction.

Calculate the velocities of each vehicle after impact if the coefficient of restitution of the vehicles' bumpers is 0.85.
That's the part where you need the mass of the car.
 
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I believe you need the mass of the car to get the drag force on it while skidding to a stop.
 
insightful said:
I believe you need the mass of the car to get the drag force on it while skidding to a stop.
No. We are given g, the coefficient of friction, and the initial and final speeds, and we wish to find a distance. None of those involves a mass dimension. Consequently (by dimensional analysis) being told one mass as well cannot be of use.
 
haruspex said:
No. We are given g, the coefficient of friction, and the initial and final speeds, and we wish to find a distance. None of those involves a mass dimension. Consequently (by dimensional analysis) being told one mass as well cannot be of use.
Oops, of course, you're right. My only defense is that the engineer in me is more comfortable going the "F=ma" route.
 

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