Runner Impulse Question: Estimate Power of Runner Leaving Blocks

[suedi]

Homework Statement

If a runner is giving the starting blocks a impulse of 150Ns for 0.4 seconds and she weighs 65kg. estimate the power [W] of the runner in the first 0.4 seconds

Relevant Equations

I=mv-mv0
Ek=mv^2/2
P=E/t

i tried to calculate the the kinetic energy by using the impulse law and got that the speed is 150Ns/65kg then I calculated the Energy and later the power. My answer is was 433Watts. How would you solve this question?

 

[erobz]

How would you solve this question?

Other than leaving everything in variables till the end, the same method as you.

 

[kuruman]

It would also be considerate if you expressed the speed in more conventional units than Ns/kg.

 

[neilparker62]

$$\frac{I^2}{2mt}$$

 

[Steve4Physics]

My answer is was 433Watts. How would you solve this question?

I would:

• derive the formula given by @neilparker62 in Post #4, clearly showing all steps
• substitute the given values
• round my answer to a suitable number of significant figures (to match the precision of the given data and the question's use of the word 'estimate')
• give the units correctly, noting that 'watt' is written all in lower case and its symbol, 'W', is written using upper case

 

[kuruman]

I wouldn't exactly call the contents of post #4 a formula because there is no "equals" sign. We see an expression which has units of ${(\text{N⋅s})}^2/\text{(kg⋅s)}$.

 

[erobz]

I wouldn't worry about it. The OP was just checking to see if ChatGPT gave them the correct answer.

 

[kuruman]

I doubt that ChaGT had anything to do with OP's answer. Just for kicks, I checked with ChatGPT and here are the results.

kuruman:
If a runner is giving the starting blocks a impulse of 150Ns for 0.4 seconds and she weighs 65kg. estimate the power [W] of the runner in the first 0.4 seconds.

ChatGPT:
To estimate the power of the runner in the first 0.4 seconds, we need to calculate the work done by the runner and then divide it by the time interval. The formula for power is:

Power = Work / Time

The work done can be calculated by multiplying the force applied by the displacement. In this case, the force applied can be determined using the impulse-momentum relationship:

Impulse = Force × Time

Rearranging the formula to solve for force:

Force = Impulse / Time

Given that the impulse is 150 Ns and the time is 0.4 seconds, we can calculate the force:

Force = 150 Ns / 0.4 sForce = 375 N

The displacement is not provided in the question, so we'll assume it is negligible for now. With this assumption, the work done is:

Work = Force × DisplacementWork = 375 N × 0 (assuming negligible displacement)Work = 0 J

Finally, we can calculate the power:

Power = Work / TimePower = 0 J / 0.4 sPower = 0 W

Therefore, the estimated power of the runner in the first 0.4 seconds is 0 watts. However, keep in mind that this calculation assumes negligible displacement. If the displacement is non-zero, it would affect the work done and subsequently the power.

It missed the point and couldn't make the necessary assumption that although the runner is a deformable body, at the time her feet lose contact with the stops the impulse delivered to her CM is equal in magnitude and opposite in direction to the impulse that she delivered to the stops.

Note the vague final statement where Chat GPT hedges its bets.

 

[haruspex]

Homework Statement: If a runner is giving the starting blocks a impulse of 150Ns for 0.4 seconds

No, you can’t provide an impulse for a period of time. An impulse is not a rate of anything. You can provide an impulse over a period of time.

 

[erobz]

I doubt that ChaGT had anything to do with OP's answer. Just for kicks, I checked with ChatGPT and here are the results.

kuruman:
If a runner is giving the starting blocks a impulse of 150Ns for 0.4 seconds and she weighs 65kg. estimate the power [W] of the runner in the first 0.4 seconds.

ChatGPT:
To estimate the power of the runner in the first 0.4 seconds, we need to calculate the work done by the runner and then divide it by the time interval. The formula for power is:

Power = Work / Time

The work done can be calculated by multiplying the force applied by the displacement. In this case, the force applied can be determined using the impulse-momentum relationship:

Impulse = Force × Time

Rearranging the formula to solve for force:

Force = Impulse / Time

Given that the impulse is 150 Ns and the time is 0.4 seconds, we can calculate the force:

Force = 150 Ns / 0.4 sForce = 375 N

The displacement is not provided in the question, so we'll assume it is negligible for now. With this assumption, the work done is:

Work = Force × DisplacementWork = 375 N × 0 (assuming negligible displacement)Work = 0 J

Finally, we can calculate the power:

Power = Work / TimePower = 0 J / 0.4 sPower = 0 W

Therefore, the estimated power of the runner in the first 0.4 seconds is 0 watts. However, keep in mind that this calculation assumes negligible displacement. If the displacement is non-zero, it would affect the work done and subsequently the power.

It missed the point and couldn't make the necessary assumption that although the runner is a deformable body, at the time her feet lose contact with the stops the impulse delivered to her CM is equal in magnitude and opposite in direction to the impulse that she delivered to the stops.

Note the vague final statement where Chat GPT hedges its bets.

I didn't think you would actually check. Do you get to tell it its incorrect?

 

[haruspex]

It missed the point and couldn't make the necessary assumption that although the runner is a deformable body, at the time her feet lose contact with the stops the impulse delivered to her CM is equal in magnitude and opposite in direction to the impulse that she delivered to the stops.

ChatGPT could counter that no information was given regarding other forces. Given an equal and opposite restraining force, no work was done.

 

[kuruman]

I didn't think you would actually check. Do you get to tell it its incorrect?

Even if I did, I wouldn't correct it. That's up to its handlers.

 

[neilparker62]

I doubt that ChaGT had anything to do with OP's answer. Just for kicks, I checked with ChatGPT and here are the results.

kuruman:
If a runner is giving the starting blocks a impulse of 150Ns for 0.4 seconds and she weighs 65kg. estimate the power [W] of the runner in the first 0.4 seconds.

Chat GPT's Maths/Science problem solving abilities are generally a disaster zone! In one problem I set, it could not even correctly factorise $x^2 -15x + 36$. I have offered my services as a Maths/Science tutor to no avail - alas Of course it's possible that this is deliberate on the part of Open AI. They perhaps don't want Chat GPT becoming the ultimate "cheat machine" for students.

 

[suedi]

I wouldn't worry about it. The OP was just checking to see if ChatGPT gave them the correct answer.

It was the final question of my course exam and my friend said that i did it wrong. So it was not ChatGPT

 

[haruspex]

It was the final question of my course exam and my friend said that i did it wrong. So it was not ChatGPT

Maybe your friend needs to post on this forum. Feel free to post your friend's solution if you would like other views of it.