Power from mass and acceleration

Click For Summary

Discussion Overview

The discussion revolves around calculating the power required for a car with a specified mass and acceleration capability. Participants explore the relationship between mass, acceleration, and power, considering factors such as traction limits and the dynamics of acceleration over time.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a scenario involving a 3,219lb car capable of accelerating at 40.2ft/s² and asks for the power required for this acceleration.
  • Another participant notes that the average acceleration is provided, but the maximum acceleration due to traction limits is not clear, suggesting that initial acceleration requires no power.
  • A participant clarifies that the 40.2ft/s² is indeed the maximum acceleration due to tire traction limits and that the 0-60 time was calculated based on this value.
  • Further calculations are provided to estimate the maximum power required to accelerate the car at the specified rate, incorporating conversions between units and the relationship between force, mass, and acceleration.
  • One participant expresses difficulty in following the calculations but appreciates the response, indicating a need for clearer explanations.
  • A later post references a similar problem involving stages of acceleration and suggests that power can be determined using a formula linked to another discussion thread.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the calculations presented, and there are varying levels of understanding regarding the mathematical details and assumptions involved in determining power requirements.

Contextual Notes

Participants mention traction limits and the distinction between average and maximum acceleration, which may affect the calculations. The discussion also references external resources for further exploration of similar problems.

LaCalia
Messages
4
Reaction score
0
Hello everyone, first post! I'm not terribly fluent in these matters, I'll say to start, but I have a problem.

If a 3,219lb car is capable of accelerating at 40.2ft/s^2, or 0-60mph in 2.19 seconds

How much power must it be capable of producing?

Thanks for your time and patience! :)
 
Physics news on Phys.org
There's not enough information. What you have is the average acceleration. What's missing is the maximum acceleration possible due to traction limits of the tires.

Technically it takes zero power for the initial acceleration from zero speed. During the period of maximum acceleration, the associated power will increase linearly with speed, since power = force x speed, and force = mass x acceleration.
 
Not sure I know what to take away from your answer, but I do wish to clarify that 40.2ft/s^2 is the maximum acceleration do to the bounds of the tires.

I calculated the 0-60 time based on that.
 
OK, so maximum acceleration = average acceleration = 40.2 ft / sec^2, due to traction limits. Then the maximum power required is the power required to accelerate a 3,219lb car at 40.2 ft / sec^2 at 60 mph. Note 1 pound mass = 1/32.174 slug (unit of mass). 1 mile = 5280 feet. 1 hour = 3600 seconds. 1 horsepower = 550 ft lb / sec. Force = mass x acceleration.

power = force x speed = ((3219/32.174) x 40.2 ) x (60 x 5280 / 3600) (1/550) ~= 643.5 rwhp (rear wheel horsepower).

It traction allowed for a greater amount of initial acceleration, the required power would be less. The math would be more complicated.
 
Last edited:
  • Like
Likes   Reactions: LaCalia
Having a little trouble following your maths, but otherwise, I am eternally grateful for your answer!

Thank you!
 
I updated my prior post to show what the constants I used in the formula are based on.
 
Ah! Well that helps a ton! A million more thanks!
 
I won't bother doing the math here, but for a similar problem where the traction is limited at the start (called stage 1 in the post linked below), then acceleration limited by power / speed (called stage 2 in the post linked to below). Given a velocity, total time, maximum acceleration, mass, ..., power could be determined using the formula for velocity (v = ... ) from the post linked to below:

https://www.physicsforums.com/threa...-power-requirement.864834/page-2#post-5443890
 

Similar threads

  • · Replies 17 ·
Replies
17
Views
1K
  • · Replies 41 ·
2
Replies
41
Views
5K
  • · Replies 27 ·
Replies
27
Views
4K
  • · Replies 15 ·
Replies
15
Views
5K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 21 ·
Replies
21
Views
2K
  • · Replies 41 ·
2
Replies
41
Views
5K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 9 ·
Replies
9
Views
9K
  • · Replies 41 ·
2
Replies
41
Views
4K