How Is Energy Dissipated When Braking a Car?

[physkid1]

1. How much energy is dissipated in braking a 1200-kg car to a stop from an initial speed of 30 m/s?



2. 1/2 mv(final)^2 - 1/2 mv(initial)^2



3. 1/2 x 1200 x 0^2 - 1/2 x 1200 x 30^2 = 540000J

is this right ? cheers

 

[PeterO]

1. How much energy is dissipated in braking a 1200-kg car to a stop from an initial speed of 30 m/s?



2. 1/2 mv(final)^2 - 1/2 mv(initial)^2



3. 1/2 x 1200 x 0^2 - 1/2 x 1200 x 30^2 = 540000J

is this right ? cheers

looks OK

 

[omoplata]

1/2 x 1200 x 0^2 - 1/2 x 1200 x 30^2 = 540000J

Shouldn't the right hand side be -540000 ?
And where did the J come from? If you don't have units in the left side of the equation, why did you put units on the right side?

 

[PeterO]

Shouldn't the right hand side be -540000 ?
And where did the J come from? If you don't have units in the left side of the equation, why did you put units on the right side?

Energy is a scalar, so is never negative [nor positive, nor up nor down nor North or any other direction] it is just a value.

The unit of energy is Joule, so a J is probably very appropriate.

 

[omoplata]

Energy is a scalar, so is never negative [nor positive, nor up nor down nor North or any other direction] it is just a value.

Scalars can be negative.

Example 1: If the potential energy due to a point mass infinity at an infinite distance is assumed to be zero, then the potential energy at a finite distance from the mass is negative.
Example 2: If the increase of kinetic energy in the car in this problem is negative, that means the energy has decreased. i.e. the car has lost energy.

Also refer to https://www.physicsforums.com/showthread.php?t=270612" thread.

The unit of energy is Joule, so a J is probably very appropriate.

The equation can be written down so the units on the left hand side and right hand side are equal, which the OP has not done. Also, the OP ignores the sign of the answer. So, technically, it is not an "equation" at all.

Getting into the habit of writing down correct equations to begin with can help students a lot, in avoiding common errors that happen because of misinterpretation of units etc.

 

[PeterO]

Scalars can be negative.

Example 1: If the potential energy due to a point mass infinity at an infinite distance is assumed to be zero, then the potential energy at a finite distance from the mass is negative.
Example 2: If the increase of kinetic energy in the car in this problem is negative, that means the energy has decreased. i.e. the car has lost energy.

Also refer to https://www.physicsforums.com/showthread.php?t=270612" thread.



The equation can be written down so the units on the left hand side and right hand side are equal, which the OP has not done. Also, the OP ignores the sign of the answer. So, technically, it is not an "equation" at all.

Getting into the habit of writing down correct equations to begin with can help students a lot, in avoiding common errors that happen because of misinterpretation of units etc.

OK try this:
By how much does the Gravitational Potential Energy of a 10 kg mass change for a trip between ground level and the top of a 12 m building?

 

[omoplata]

OK try this:
By how much does the Gravitational Potential Energy of a 10 kg mass change for a trip between ground level and the top of a 12 m building?

The potential energy change is approximately 10 kg * 9.81 m/s^2 * 12m.

What's your point?

 

[PeterO]

The potential energy change is approximately 10 kg * 9.81 m/s^2 * 12m.

What's your point?

I was interested to see if you fill a calculation up with units as you go - you apparently do; never seen anyone else do that - and I was also interested to see if you would first want to know whether the mass was going from the ground to the building, or the building to the ground - which didn't worry you.

 

[omoplata]

I was interested to see if you fill a calculation up with units as you go - you apparently do; never seen anyone else do that - and I was also interested to see if you would first want to know whether the mass was going from the ground to the building, or the building to the ground - which didn't worry you.

I sometimes don't use units either. But I always have the left and right sides of an equation balanced, and that includes the units.

Because the question didn't state whether it was going up or down, I simply assumed that they are asking for the numerical value of the energy change.

 

[Ignea_unda]

Shouldn't the right hand side be -540000 ?
And where did the J come from? If you don't have units in the left side of the equation, why did you put units on the right side?

Very simple - yes, by the calculation there should be a negative sign on the other side of the equation. However, that is the energy removed from the car. Thus, the energy dissipated by the brakes is the positive value of that.