question about work

[LBT]

Hi everybody,

I just do not understand, at all, the answer and the way to go trough it.

Question: How much work is done by a parachute to bring a 60 kg skydiver from his terminal velocity of 60 m/s down to 10 m/s, over period of 10 s?

My wrong answer:
W = delta KE
W = KE final -KE initial
W = 1/2*60kg*60m/s*60m/s - 1/2*60kg*10m/s*10m/s
W = 108000 - 3000
W = 105000 N

Unfortunately this is not the good answer. Rather it is 210000 N.

Do my answer is in fact the net work of the whole system, and not precisely the one of the parachute?
How can we solve this problem?

thank a lot

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[bjb305]

ok so looking at it i would have thought of the same thing.. but since it's twice as much as your answer here's my thought:
during the time it takes to slow the person down, gravity is ALSO doing that SAME amount of work, just in the opposite direction. so to actually slow the person down, you have to be cancel out gravity's work which will stop acceleration, then you have to add more to slow down from there. make sense?

 

[ChinaDoll]

1. we need to calculate delta KE like you did - 105000 N
2. we need to calculate mgh because the gravity is pulling down
delta h = (v2 - v2)/2g = 178.6
mgh = 60x9.8x178.6 = 1049999 N

Total equals 210000 N

hope it helps

 

[G1SG2]

Hi everybody,

I just do not understand, at all, the answer and the way to go trough it.

Question: How much work is done by a parachute to bring a 60 kg skydiver from his terminal velocity of 60 m/s down to 10 m/s, over period of 10 s?

My wrong answer:
W = delta KE
W = KE final -KE initial
W = 1/2*60kg*60m/s*60m/s - 1/2*60kg*10m/s*10m/s
W = 108000 - 3000
W = 105000 N

Unfortunately this is not the good answer. Rather it is 210000 N.

Do my answer is in fact the net work of the whole system, and not precisely the one of the parachute?
How can we solve this problem?

thank a lot

Hmm, I used a kinematic equation to find the distance x=avg v*t, which came out to be 350 m. Then I found the work done by gravity which I thought would=work done by the parachute, so W=F*D, W=mg*d, W=(60 kg)*(g) *(350m)=210 x 10^3 N. Not sure if my reasoning of the work done by gravity=work done by parachute is entirely correct...

 

[Will Hunting]

Hi everybody,

I just do not understand, at all, the answer and the way to go trough it.

Question: How much work is done by a parachute to bring a 60 kg skydiver from his terminal velocity of 60 m/s down to 10 m/s, over period of 10 s?

My wrong answer:
W = delta KE
W = KE final -KE initial
W = 1/2*60kg*60m/s*60m/s - 1/2*60kg*10m/s*10m/s
W = 108000 - 3000
W = 105000 N

Unfortunately this is not the good answer. Rather it is 210000 N.

Do my answer is in fact the net work of the whole system, and not precisely the one of the parachute?
How can we solve this problem?

thank a lot

You must think carefully. deltaKE=NET Work

Parachute is not net work. Remember when something is falling you MUST take gravity into account. Think about, when something falls normally it gains KE and loses mgh. However, here it is losing both. Remember total is conserved, think of the parachute as "friction." mgh is only against gravity, here it isn't valid. G is the acceleration. The acceleration here is not g it's 5. Since that's the rate it's falling with.

Kei + PEi - workParachute= Kef + mghi
so Kei-Kef + Pei - Pef= work parachute

so calculating deltaKe is easy 105,000. However, you must determine the height. It's 350 as you stated *5*60=105,000

You can't use 10. The only way to use 10 is to realize that you have to half the distance. So, 10 is conceptually incorrect since the distance is 350 and NOT 175. The whole point of the shoot is to increase the distance of velocity slowing. So the trick is to realize that mgh=mad =force*d and here h=d and a =5 and not 10. If a was 10 then the dude would NOT slow down. Excellent problem. So, 60*10*350 is wrong. it's 105000 from KE + 60*5*350. HTH

Will Hunting

 

[Will Hunting]

Hi everybody,

I just do not understand, at all, the answer and the way to go trough it.

Question: How much work is done by a parachute to bring a 60 kg skydiver from his terminal velocity of 60 m/s down to 10 m/s, over period of 10 s?

My wrong answer:
W = delta KE
W = KE final -KE initial
W = 1/2*60kg*60m/s*60m/s - 1/2*60kg*10m/s*10m/s
W = 108000 - 3000
W = 105000 N

Unfortunately this is not the good answer. Rather it is 210000 N.

Do my answer is in fact the net work of the whole system, and not precisely the one of the parachute?
How can we solve this problem?

thank a lot

where did you get this?

 

[LBT]

In a Kaplan exercices book.

Thank you a lot

Louis