/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 BIO How High Can We Jump? The ma... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

BIO How High Can We Jump? The maximum height a typical human can jump from a crouched start is about 60 \(\mathrm{cm}\) . By how much does the gravitational potential energy increase for a 72 -kg person in such a jump? Where does this energy come from?

Short Answer

Expert verified
The gravitational potential energy increases by 423.36 J, and the energy comes from the chemical energy in muscles.

Step by step solution

01

Identify the Known Values

The problem gives the maximum height a person can jump, which is 60 cm, and the person's mass, which is 72 kg. We need to convert the height to meters: 60 cm = 0.6 m.
02

Recall the Gravitational Potential Energy Formula

The gravitational potential energy (GPE) is given by the formula:\[GPE = m \cdot g \cdot h\]where \(m\) is mass, \(g\) is acceleration due to gravity (9.8 m/s²), and \(h\) is height.
03

Calculate the Change in Gravitational Potential Energy

Substitute the given values into the formula for GPE:\[GPE = 72 \text{ kg} \times 9.8 \text{ m/s}^2 \times 0.6 \text{ m}\]Calculate the result:\[GPE = 72 \times 9.8 \times 0.6 = 423.36 \text{ J}\]The gravitational potential energy increases by 423.36 Joules.
04

Explain the Source of Energy

The energy required for the jump comes from the chemical energy stored in the muscles of the person. This energy is converted into kinetic energy and subsequently into gravitational potential energy during the jump.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Energy Conversion
Gravitational potential energy is a wonderful example of energy conversion. This concept is all about changing one form of energy into another. When we talk about jumping, it involves a fascinating transformation of energy. Initially, a person uses chemical energy stored in their muscles. This chemical energy is generated by breaking down molecules like glucose.

When you initiate a jump, the muscles convert this stored chemical energy into kinetic energy, which is the energy of motion. As the body rises, kinetic energy gradually transforms into gravitational potential energy. This is the stored energy an object has due to its height above the ground.

The conversion does not stop here either. When the person lands, the gravitational potential energy is transformed back into kinetic energy. Eventually, some of this energy becomes sound energy as your feet hit the ground, and thermal energy when your body absorbs the impact.
Human Biomechanics
Jumping is not just an art; it’s a science! Involving intricate mechanics of the human body, it showcases biomechanics at its finest. Biomechanics examines the physical aspects of living organisms. It combines principles from mechanics and biology to understand how muscles, bones, and joints work together.

Starting in a crouched position, a human jump involves multiple muscle groups. Key players include your calf muscles, hamstrings, and glutes, which collectively produce force. The crouch allows muscles to stretch before contraction, creating a spring effect.

Upon jumping, the muscles contract swiftly. This contraction produces enough force to momentarily lift the body's weight against gravity. The synchronization of muscle contractions and joint flexion achieves maximum height, around 60 cm for a typical person.
  • Muscle strength, as well as muscle timing, are crucial for an effective jump.
  • Better muscle coordination can help improve the efficiency of the jump.
  • Understanding biomechanics can aid in enhancing athletic performance.
Physics Problem Solving
Solving physics problems can help demystify everyday phenomena. To tackle them effectively, breaking the problem down into manageable steps is key, as seen in calculating the increase in gravitational potential energy during a jump.

To begin with, identify the known quantities like height and mass, as given in our jumping exercise. Converting them into compatible units ensures there are no errors. This is critical in all physics problems.

With all values in place, apply the proper formula. Here, it is the gravitational potential energy formula: \[ GPE = m \cdot g \cdot h \]Substituting the values into the equation gives the increase in potential energy, which is 423.36 Joules.

Lastly, one should always consider the source of energy. In physics, knowing where energies originate and how they transform helps create a fuller understanding of the process. Efficient problem-solving involves understanding concepts deeply and using systematic approaches.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A truck with mass \(m\) has a brake failure while going down an icy mountain road of constant downward slope angle \(\alpha\) (Fig. \(\mathrm{P} 7.66\) ). Initially the truck is moving downhill at speed \(v_{0}\) . After careening downhill a distance \(L\) with negligible friction, the truck driver steers the runaway vehicle onto a runaway truck ramp of constant upward slope angle \(\beta\) . The truck ramp has a soft sand surface for which the coefficient of rolling friction is \(\mu_{\mathrm{r}}\) . What is the distance that the truck moves up the ramp before coming to a halt? Solve using energy methods.

An empty crate is given an initial push down a ramp, starting with speed \(v_{0,}\) and reaches the bottom with speed \(v\) and kinetic energy \(K .\) Some books are now placed in the crate, so that the total mass is quadrupled. The coefficient of kinetic friction is constant and air resistance is negligible. Starting again with \(v_{0}\) at the top of the ramp, what are the speed and kinetic energy at the bottom? Explain the reasoning behind your answers.

Two blocks with different masses are attached to either end of a light rope that passes over a light, frictionless pulley suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended \(1.20 \mathrm{m},\) its speed is 3.00 \(\mathrm{m} / \mathrm{s} .\) If the total mass of the two blocks is 15.0 \(\mathrm{kg},\) what is the mass of each block?

A 60.0 -kg skier sturts from rest at the top of a ski slope 65.0 \(\mathrm{m}\) high. (a) If frictional forces do \(-10.5 \mathrm{kJ}\) of work on her as she descends, how fast is she going at the bottom of the slope? (b) Now moving horizontally, the skier crosses a patch of soft snow, where \(\mu_{\mathrm{k}}=0.20 .\) If the patch is 82.0 \(\mathrm{m}\) wide and the average force of air resistance on the skier is 160 \(\mathrm{N}\) , how fast is she going after crossing the patch? (c) The skier hits a snowdrift and penetrates 2.5 \(\mathrm{m}\) into it before coming to a stop. What is the average force exerted on her by the snowdrift as it stops her?

EP Pendulum. A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 \(\mathrm{m}\) to form a pendulum. The pendulum is swinging so as to make a maximum angle of \(45^{\circ}\) with the vertical. Air resistance is negligible. (a) What is the speed of the rock when the string passes through the vertical position? (b) What is the tension in the string when it makes an angle of \(45^{\circ}\) with the vertical? (c) What is the tension in the string as it passes through the vertical?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.