# 30,000 fleas jumping off an elephant

• owtu
In summary, the problem involves a flea-infested elephant standing on a frozen lake, with 30,000 fleas jumping off its back per second in a horizontal direction with a velocity of 10 m/s. Using conservation of momentum, the final velocity of the elephant can be calculated to be 1.7 x 10^(-4) m/s. This is assuming the elephant is infested with 30,000 fleas and they all jump off at the same time and in the same direction. The reasoning behind this calculation involves following a pattern for conservation problems and considering the net momentum of the elephant and fleas before and after the fleas jump off.
owtu

## Homework Statement

A flea infested elephant with a mass of 3500 kg is standing on a frozen lake wearing frictionless ice skates. If 30000 fast fleas jump off the elephants back (in a horizontal direction) per second, and each flea jumps with a velocity of 10 m/s find the velocity of the elephant using conservation of momentum. Each flea has a mass of 10 milligrams

v2 = 2m1/(m1+m2)

## The Attempt at a Solution

I converted 10 milligrams to kg and multiplied by 30,000 and got .3 kg. I imagined this as an elastic collision of a .3 kg object hitting the elephant at 10 m/s. So, solving for the elephants final velocity.

v2 = 2(.3)/ (3500+.3)
v2 = .6/(3500.3)
v2 = 1.7 x 10^(-4) m/s

is this correct?

Keep that up for an hour or so, and the elephant has lost it's entire weight in fleas!

I don't see the reasoning.
Your first line seems to suggest that the elephant and a whole seconds worth of fleas are moving at speed v2 as a result of one seconds worth of fleas jumping off at speed 2 units.

Notice that we are not told how many fleas are infesting the elephant, so you'll need to make an approximation.
Also - why wouldn't the elephant accelerate?

ignore how many fleas are infesting the elephant. for this problem we're supposed to assume it is infested with 30,000 fleas and they all jump off the elephant in the same horizontal direction with the same speed and at the same time

Your first line seems to suggest that the elephant and 30000 fleas are moving at speed v2 as a result of 30000 fleas jumping off at speed 2 units.

No, the elephant is stationary. the fleas are moving at speed v1 and I'm trying to solve for the final speed of the elephant, v2

You gave me:
v1=10m/s (speed of fleas)
m=0.3kg (mass of 30000 fleas)
M=3500kg (mass of elephant)

Then you wrote: v2 = 2(.3)/ (3500+.3)

so v2= 2m/(M+m) or (M+m)v2=2m ... the dimensions don't match.

But why would you try that in the first place?
What was your reasoning? I won't be able to help you very well if I don't know how you think.

When you do conservation problems, you follow a pattern.
This is conservation of momentum: so ...
Do you know the equation for the momentum of something?
Do you know the expression for conservation of momentum?

Before the fleas jump off, what is the net momentum of elephant + fleas?

After the fleas jump off, the elephant and fleas move in opposite directions ... write expressions for the momentum of the elephant and the momentum of the fleas ... and thus, the net momentum.

From conservation of momentum, write down an expression which relates the momentum before to the momentum after.

Solve for v2.

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## What is the significance of 30,000 fleas jumping off an elephant?

The number of fleas jumping off an elephant may seem like a lot, but it is actually a normal occurrence for elephants living in the wild. This phenomenon is known as "ecological balance" and it helps to keep the elephant and its environment healthy.

## Why do fleas jump off elephants?

Fleas jump off elephants as a natural survival instinct. Elephants are known to carry a large number of fleas on their bodies, and when the population becomes too high, the fleas will jump off in search of a new host. This helps to prevent overpopulation and ensures that the fleas have access to resources and breeding opportunities.

## Can fleas harm elephants?

Fleas are not a serious threat to elephants and do not cause any significant harm. However, a large number of fleas can cause irritation and discomfort for the elephant, leading to excessive scratching and potential skin infections. This is why fleas jumping off an elephant can be beneficial for both the elephant and the flea population.

## Do fleas have any benefits for elephants?

While fleas may seem like a nuisance, they actually provide some benefits for elephants. Fleas act as natural groomers, cleaning the elephant's skin and removing dead skin cells and debris. They also serve as a food source for other animals, contributing to the overall balance of the ecosystem.

## Is there a way to prevent fleas from jumping off elephants?

It is not necessary to prevent fleas from jumping off elephants, as it is a natural and necessary process for both the elephant and the flea population. However, if excessive flea populations become a concern for the health of the elephant, there are methods of flea control that can be implemented, such as using natural predators or limiting the elephant's contact with other animals that may carry fleas.

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