Calculate Energy Needed to Move 1000lb Vehicle at 55mph for 1hr

In summary: Therefore the energy required to move the car at 55mph for 1 hour would be approximately 1.76 * 10^6 J.
  • #1
lex_ee
1
0
I'd like to calculate the energy required to move a 1000lb vehicle at 55mph for 1hr. I'm looking for a simple calculation, nothing with drag, friction or acceleration is required

I expect this to be pretty simple, 1/2*m*v^2, to solve for the Kinetic Energy of the vehicle. However, how does 'time' come into play, to determine the energy needed over time?

Thanks
 
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  • #2
If there is no drag or friction, once your car is going 55 mph it will need no energy to keep going at that speed.
 
  • #3
lex_ee said:
I'd like to calculate the energy required to move a 1000lb vehicle at 55mph for 1hr. I'm looking for a simple calculation, nothing with drag, friction or acceleration is required

I expect this to be pretty simple, 1/2*m*v^2, to solve for the Kinetic Energy of the vehicle. However, how does 'time' come into play, to determine the energy needed over time?

Thanks
If there are no non-conservative forces acting on the car, then maintaining a constant velocity won't take any energy.
Taking drag into account is relatively simple actually.
Use the work-energy theorem [itex]W=\Delta E[/itex] and the definition of work
[tex]W=\int_a^b \vec F \cdot \vec{dx}[/tex].
The drag equation tells us that [itex]F_d=-\frac{1}{2}\rho A C_d v^2[/itex]. You can look this up on wikipedia for the details.
Now you told us that the velocity needed to be a constant we can pull it out of the work integral and get (evaluating between x=0 and x=x),
[tex]W=\frac{1}{2}\rho A C_d v^2 x[/tex]
where x is the total distance traveled.
Now [itex]v=\frac{dx}{dt}[/itex] and with v constant, [itex]x=vt[/itex] and so we see the total work done is proportional to [itex]v^3[/itex],
[tex]W=\frac{1}{2}\rho A C_d v^3 t[/tex].
For a reasonable car and under normal atmospheric conditions,
[itex]C_dA\approx 7 m^2[/itex],
[itex]\rho\approx 1.2 kg/m^3[/itex].
So the work done after an amount of time t is numerically approximately (for normal cars, see the ACd product for cars on wikipedia),
[tex]W\approx 5v^3t[/tex].
For a car going 55 mph for 3600 s, the work is approximately [itex] 3 10^8 J[/itex]. That's quite a bit of energy!
Hope that helps.
 
  • #4
mathman said:
If there is no drag or friction, once your car is going 55 mph it will need no energy to keep going at that speed.

I agree. lex_ee, your result will be overly-simplistic. You can find dynamometer data online for most cars. The data will give you rpms (or mph) and power in a more realistic setting--if you are given rpms, you will need appropriate car specs and data to convert to mph:
http://www.type2.com/library/misc/calcspd.htm

The power can then be converted into the quantity that you desire.
 
  • #5
lex_ee said:
I'd like to calculate the energy required to move a 1000lb vehicle at 55mph for 1hr. I'm looking for a simple calculation, nothing with drag, friction or acceleration is required

I expect this to be pretty simple, 1/2*m*v^2, to solve for the Kinetic Energy of the vehicle. However, how does 'time' come into play, to determine the energy needed over time?

Thanks

By Newton's first law once the car is moving at 55mph you will not need to add any more energy as you will not be accelerating it any more.

[tex]K=\frac{1}{2}mv^{2}[/tex]

[tex]\Delta{K} = \frac{1}{2}m(\Delta{v})^{2}[/tex] as [tex]\frac{dm}{dt}[/tex] is constant

[tex]\approx\frac{1}{2}(\frac{1000}{2.2})(55*1.6)^{2}[/tex]

[tex]\approx\1.76 * 10^{6} [/tex] J
 
Last edited:

FAQ: Calculate Energy Needed to Move 1000lb Vehicle at 55mph for 1hr

What is the formula for calculating the energy needed to move a 1000lb vehicle at 55mph for 1 hour?

The formula for calculating energy is E=mv^2, where E is energy, m is mass, and v is velocity. To calculate the energy needed for this scenario, we would use the formula E = (1000lbs)(55mph)^2 = 3,025,000 ft-lbs.

What units of measurement should be used for this calculation?

The units of measurement used should be consistent throughout the formula. In this case, the mass should be in pounds and the velocity should be in miles per hour. The resulting energy will be in foot-pounds (ft-lbs).

How does the weight of the vehicle affect the energy needed for movement?

The weight of the vehicle directly affects the energy needed for movement. The heavier the vehicle, the more energy is required to move it at a certain speed. In this scenario, a 1000lb vehicle will require more energy than a 500lb vehicle to travel at the same speed for the same amount of time.

What other factors may impact the amount of energy needed for movement?

Other factors that may impact the energy needed for movement include air resistance, friction from the road, and changes in elevation. These factors may increase or decrease the overall energy needed to move the vehicle.

How is this calculation useful for scientists and engineers?

This calculation is useful for scientists and engineers in a variety of fields, such as transportation, energy, and mechanics. It can help determine the amount of energy needed for different vehicles and modes of transportation, as well as inform design choices for more efficient and sustainable options.

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