Scaling and Proportion Physics problem. ?

In summary, by magnifying a flea by a factor of 700, its jumping height would increase by a factor of 7003, resulting in a maximum jumping height of 0.117 m.
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Scaling and Proportion Physics problem. Please Help!?

1.

A flea is able to jump straight up about 0.44 m. It has been said that if a flea were as big as a human, it would be able to jump over a 100-story building! When an animal jumps, it converts work done in contracting muscles into gravitational potential energy (with some steps in between). The maximum force exerted by a muscle is proportional to its cross-sectional area, and the work done by the muscle is this force times the length of contraction. If we magnified a flea by a factor of 700, the cross section of its muscle would increase by 700^2 and the length of contraction would increase by 700. How high would this "superflea" be able to jump? (Don't forget that the mass of the "superflea" increases as well.)

My attempt:
The muscle cross section increases by 700^2 = 490000. The energy stored in the muscle increases by area x length = 700^3 = 343 000,000. The flea's mass increases by the cube of length, or the same ratio, 343,000,000.
m= 0.44^3
= 0.085184
M g H = stored muscle energy.
H = 343 000,000/ (0.085184)(9.8)
= 4.1 x 10^8

H, the jumping height, is proportional to
(stored muscle energy/M)
and this ratio does not change. Neither does the height that it can jump.

I AM REALLY CONFUSED! PLEASE HELP ME WITH MY METHOD BECAUSE I THINK IM DOING IT WRONG
 
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  • #2
. Answer:The formula for the maximum jumping height is:H = (stored muscle energy/M)*gWhere H is the maximum jumping height, M is the mass of the flea, and g is the acceleration due to gravity (9.8 m/s2).In this problem, the mass of the flea increases by a factor of 343 000,000, while the stored energy increases by a factor of 7003.Plugging in these values into the equation, we get:H = (7003*0.44^3/343 000,000)*9.8H = 0.117 mTherefore, the "superflea" would be able to jump 0.117 m high.
 

1. What is scaling and proportion in physics?

Scaling and proportion in physics refers to the relationship between two sets of measurements or quantities. It is used to determine how a change in one variable affects another variable.

2. How do you solve a scaling and proportion physics problem?

To solve a scaling and proportion physics problem, you must first identify the two variables and their corresponding values. Then, you can set up a proportion by cross-multiplying the values and solving for the unknown variable.

3. Can scaling and proportion be applied to all types of physics problems?

Yes, scaling and proportion can be applied to various types of physics problems, such as distance, time, velocity, and force. It is a fundamental concept in physics that helps to establish relationships between variables.

4. What are some real-life examples of scaling and proportion in physics?

Some real-life examples of scaling and proportion in physics include calculating the speed of a moving car, determining the force needed to lift an object, and predicting the distance an object will travel when thrown at a certain angle and velocity.

5. How important is understanding scaling and proportion in physics?

Understanding scaling and proportion in physics is crucial as it helps to solve complex problems and make accurate predictions. It is also a fundamental concept in many other sciences, such as chemistry and biology, making it essential for a deeper understanding of the natural world.

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