Stopping distance (work & energy)

• Chica1975
In summary, when making an emergency stop on a level dry concrete road, the magnitude of the friction force is approximately 80% of the weight of the vehicle. To calculate the stopping distance for a vehicle traveling at 88km/h, all wheels are assumed to be locked and 9.8 m/s2 is used for gravitational acceleration. Using the work-energy theorem, the initial kinetic energy of the car is related to the work done by friction in stopping the car. However, the specific formula to calculate the stopping distance is still unclear.
Chica1975

Homework Statement

in an emergency stop on a level dry concrete road the magnitude of the friction force when sliding is approx 80% of the weight of the vehicle. What stopping distance is required for a vehicle traveling at 88km/h (24.444 m.s)?

Assume that all the wheels lock when the brakes are applied

Use 9.8 m/s2 for gravitational acceleration

W= F*X
.5mvE2
SumF = ma

The Attempt at a Solution

I have tried a number of combinations using the above equations - I can't figure this out.

Help anyone!

Show what you tried. Hint: Use the work-energy theorem.

basically I tried using each of the above and nothing worked I even tried .5mvfE2 -.5mv0E2 - nothing works

Use my hint! (You need another formula that combines your first two.)

is it potential energy? PE = mgh?

a bit lost

Chica1975 said:
is it potential energy? PE = mgh?
No. Gravitational PE is not relevant here since the height doesn't change.

How does the initial KE of the car relate to the work done by friction in stopping the car?

to be honest I don't know - it must reduce kinetic energy or change it in some way becoz friction is going in the opposite direction?

I am completely lost.

1. What is stopping distance?

The stopping distance is the distance a moving object travels before coming to a complete stop. It takes into account both the distance traveled during the reaction time of the driver and the distance traveled while braking.

2. How is stopping distance affected by speed?

The higher the speed of the object, the longer the stopping distance will be. This is because the object has more kinetic energy, which must be dissipated in order to come to a stop. As the speed increases, so does the amount of kinetic energy and therefore the amount of work required to stop the object.

3. What is the relationship between stopping distance and work?

The stopping distance is directly proportional to the work done to stop the object. This means that as the stopping distance increases, so does the amount of work done to stop the object. Similarly, if the stopping distance decreases, the work done will also decrease.

4. How does friction affect stopping distance?

Friction plays a crucial role in determining the stopping distance of an object. Friction between the tires and the road surface helps to slow down the object by converting its kinetic energy into heat. The higher the friction between the tires and the road, the shorter the stopping distance will be.

5. What other factors can affect stopping distance?

Apart from speed and friction, there are several other factors that can affect stopping distance. These include the type and condition of the road surface, the condition of the tires, the weight and size of the object, and the conditions of the weather. All of these factors can impact the amount of work and energy required to bring an object to a stop.

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