Constant power, resistance, work, energy

In summary, the car has a mass of 1200 kg and a constant power output of 20kw. It experiences a resistance of 500N while traveling with speeds of 10 m/s and 25 m/s at points X and Y, respectively. It takes 30.5 seconds to travel from X to Y. The acceleration of the car at point X is 2.083 m/s^2. Considering work and energy, the distance traveled from X to Y is approximately 470 m.
  • #1
Demonfruzz
9
0

Homework Statement


Mass car 1200 kg .

power car constant 20kw .

Resistance car motion 500N.

Car passes point X and Y with speeds 10 m/s ,25 m/s.

Car takes 30.5 s to travel from X to Y

1. Find acc of car at x
2.considering work/energy find distance XY

Homework Equations

The Attempt at a Solution

 
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  • #2
T
Demonfruzz said:

Homework Statement


Mass car 1200 kg .

power car constant 20kw .

Resistance car motion 500N.

Car passes point X and Y with speeds 10 m/s ,25 m/s.

Car takes 30.5 s to travel from X to Y

1. Find acc of car at x
2.considering work/energy find distance XY

Homework Equations

The Attempt at a Solution

tried a few but looks nowhere near promising and I don't have an answer for the question ,past year examinations
 
  • #3
It is difficult to provide you any guidance if you do not show us your work. Please post your attempt at a solution, no matter how incorrect you may think it is.
 
  • #4
You might start by finding the net driving force at point A ( car driving force = power (watts) / velocity (m/s) )
The acceleration at that point = net force / mass

Hint: A velocity v acceleration graph covering the speed range will be a curve
 
  • #5
1. Distance used from question 2.
work = force x distance
Force =610KJ/470 m
=1297.9
acceleration = force/mass
=1297.9/1200
=1.0815

2. Power x time = work
Work= 20kw x 30.5
=610kj

Resistance = 500N x distancexy

Net =kinetic energy
610kj - (500N x distancexy )= (0.5 )
(1200)
(25^2)

Therefore distance xy = 470 m
 
  • #6
This looks like a calculus solution
 
  • #7
By short step excel based start and step program i get around 293 m distance
 
  • #8
dean barry said:
You might start by finding the net driving force at point A ( car driving force = power (watts) / velocity (m/s) )
The acceleration at that point = net force / mass

Hint: A velocity v acceleration graph covering the speed range will be a curve

Hmm I see I will try to work it out , thanks for the help
 
  • #9
The program consides short velocity changes, adding the derived distance changes as it goes.
Consider the velocity change between 10 m/s and 11 m/s, calculate the (net) driving force at each velocity, find the average (net) force, calc the acceleration from : a = f net ave / mass, then use newons laws to calculate the distance traveled between those two velocities.
Add the steps as you go for a running distance.
Hint: i used steps of 0.01 metres / second, and 1500 ish lines of program
 
  • #10
Sorry am not really sure about calculus part
But maybe this is the solution

Driving force =1200*acc - 500N
P=fv
20kw=1200*acc - 500N
Acc=2.083

2.
Driving force =1200(2.083)- 500
=1999.6

Fs=0.5mv^2 - 0.5 mu^2
S={ [(0.5)(1200)(25^2)-[(0.5)(1200)(10^2)]} / driving force

Therefore distance =157.6m
 
  • #11
Demonfruzz said:
2. Power x time = work
Work= 20kw x 30.5
=610kj

Resistance = 500N x distancexy

Net =kinetic energy
610kj - (500N x distancexy )= (0.5 ) (1200) (25^2)

Therefore distance xy = 470 m
You are almost right.

net work done = change in KE
and the car already has some KE at the beginning of that 30.5s time interval.
 
  • #12
Demonfruzz said:
Fs=0.5mv^2 - 0.5 mu^2

I don't think that this is correct, being as the force that propels the car forward is not constant.

Demonfruzz said:
Driving force =1200*acc - 500N
P=fv
20kw=1200*acc - 500N
Acc=2.083

A power output is not a force.
 
  • #13
Ao
NascentOxygen said:
You are almost right.

net work done = change in KE
and the car already has some KE at the beginning of that 30.5s time interval.
So the 2nd answer i gave should be the correct one ?

Thanks
 
  • #14
Demonfruzz said:
So the 2nd answer i gave should be the correct one ?
No, because you introduced other mistakes there. :frown:

Fix the one I commented on.
 
  • #15
NascentOxygen said:
No, because you introduced other mistakes there. :frown:

Fix the one I commented on.

Yea I thought the 2nd answer was correct because it fixes the change in kinetic energy as you had pointed out
 
  • #16
Demonfruzz said:
But maybe this is the solution

Driving force =1200*acc - 500N
P=fv
20kw=1200*acc - 500N
Acc=2.083
you wrote, correctly, P=F v, but that's not what you did in the next step. What happened to v?
 
  • #17
haruspex said:
you wrote, correctly, P=F v, but that's not what you did in the next step. What happened to v?

Owh sorry I made a typo I did include the v in the calculation
V = 10 at x
20k=(1200*accleration - 500 ) (10 ) Acc= 2.083
 
  • #18
Demonfruzz said:
Owh sorry I made a typo I did include the v in the calculation
V = 10 at x
20k=(1200*accleration - 500 ) (10 ) Acc= 2.083
Subtracting the 500N resistance made the acceleration go up. Does that seem reasonable?
 
  • #19
Thanks got it guys , conceptual problem
 

FAQ: Constant power, resistance, work, energy

What is constant power?

Constant power is the rate at which work is done or energy is transferred. It is measured in watts (W) and is equal to the product of voltage and current.

How does resistance affect power?

Resistance is a measure of how difficult it is for current to flow through a material. The higher the resistance, the lower the power output. This is because resistance causes a decrease in current, which in turn decreases the rate at which work is done.

What is work and how is it related to energy?

Work is the amount of energy transferred when a force is applied over a certain distance. It is measured in joules (J). Work and energy are directly related, as work is a form of energy and can be converted into other forms of energy, such as kinetic or potential energy.

How is energy calculated?

Energy is calculated by multiplying power by time. This is because power is the rate at which energy is transferred, and time is the duration of the transfer. The unit of energy is the same as work, joules (J).

What is the difference between kinetic and potential energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on the mass and velocity of the object. Potential energy, on the other hand, is the energy an object has due to its position or state. It can be gravitational potential energy, elastic potential energy, or chemical potential energy.

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