The maximum height a typical human can jump from a crouched start...

Question

The maximum height a typical human can jump from a crouched start is about 60 cm. By how much does the gravitational potential energy increase for a 72-kg person in such a jump? Where does this energy come from?

Accepted Answer

Hey everyone. So today we're dealing with the problem about potential and kinetic energy. So we're being told an adult grasshopper can jump a height of cm 50 cm. And based on this we're being asked asked two separate questions in a sense. First were being asked what is the increase in gravitational potential energy for a 0.25 g grasshopper in this situation and to what is the origin of this energy? So, let's start with the second part. First, we're talking about a grasshopper and let's just draw it out here. If we have a grasshopper on the ground and let's just say this is our grasshopper, if it's jumping it's at rest currently. Which means there's no motion, there's no energy of motion. So if it's starting at rest and then jumps and then comes back down. That means the origin of the motion must come from elastic potential energy stored in the grasshoppers muscles. It's not already in motion. When we come to its problem, we're talking about it. Going from a static state, jumping up and then coming back down. So in this case we can eliminate answer choice is let's use red. We can eliminate answer choices. Be anti because they both site kinetic potential energy. Or sorry, kinetic potential energy, which doesn't make much sense. And kinetic energy stored in the grasshoppers muscles. No. With this in mind let's go ahead and take a better look at the grasshoppers motion itself. Well, the And let me draw it again over here, we have the grasshopper, we have our little grasshopper. Now, if he jumps the height of 50 cm he jumps a height. And let's draw that out here. The height he jumps height is equal to 50 centimeters. And we can recall that the for gravitational potential energy. The formula for it is M G delta Y. Where delta Y. Is the change in height. We also know that G. is the force or the acceleration due to gravity. It is 9.8 one m/s squared. And with that in mind, let's go ahead and sort of plug in our values. Now for the gravitational potential energy, we get that The mass is 0.25 g. And we want this in kilograms because again, we use S. A standard units. Yeah. S. A units. For most of our calculations unless otherwise specified. So we can also recall a conversion factor that states that we have 10 or sorry, one kg for every 10 to the third grams. For every 1000 g we have one kg We have the acceleration due to gravity which is 9.81 m/s squared. And the change in height the delta. Why is 50 centimeters again? We want this in S. I. Units. So meters in which we can recall that for every one m, there are 100 centimeters or 10 to the second centimeters simplifying all this. And solving, we get a final answer Of 1. times 10 to the -3 jewels, which is also the same as 0.1 - two jewels. Therefore, the increase in gravitational potential energy for a 0.25 g Grasshopper is 0.122 jewels, and the energy comes from elastic potential energy stored in the grasshoppers muscles. This corresponds with answer choice a. I hope this helps, and I look forward to seeing you all in the next one.

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