Ch 10: Interactions and Potential Energy

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo

Knight Calc 5th Edition

Ch 10: Interactions and Potential Energy

Problema 23

Capitolo 10, Problema 23

The elastic energy stored in your tendons can contribute up to 35% of your energy needs when running. Sports scientists find that (on average) the knee extensor tendons in sprinters stretch 41 mm while those of nonathletes stretch only 33 mm. The spring constant of the tendon is the same for both groups, 33 N/mm. What is the difference in maximum stored energy between the sprinters and the nonathletes?

Guida verificata passo dopo passo

The elastic potential energy stored in a spring (or tendon, in this case) is given by the formula:

U_{elastic} = \frac{1}{2} k x^{2}

, where

k

is the spring constant and

x

is the stretch (displacement) of the spring.

Substitute the given values for the sprinters into the formula. The spring constant is

k = 33

N/mm, and the stretch is

x = 41

mm. The elastic energy for sprinters is:

U_{sprinters} = \frac{1}{2} k x^{2}

Substitute the given values for the nonathletes into the formula. The spring constant is the same,

k = 33

N/mm, and the stretch is

x = 33

mm. The elastic energy for nonathletes is:

U_{nonathletes} = \frac{1}{2} k x^{2}

To find the difference in maximum stored energy between the sprinters and the nonathletes, calculate:

ΔU = U_{sprinters} - U_{nonathletes}

. Substitute the expressions for

U_{sprinters}

and

U_{nonathletes}

into this equation.

Simplify the expression for

ΔU

to find the difference in elastic energy. Ensure that the units are consistent throughout the calculation (N·mm or J).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Elastic Potential Energy

Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing. It can be calculated using the formula E = 1/2 k x², where E is the elastic potential energy, k is the spring constant, and x is the displacement from the equilibrium position. This concept is crucial for understanding how tendons store energy during activities like running.

Video consigliato:

Percorso guidato

07:24

Potential Energy Graphs

Spring Constant

The spring constant, denoted as k, is a measure of a spring's stiffness, defined as the force required to stretch or compress the spring by a unit distance. In this context, the spring constant of the tendons is the same for both sprinters and nonathletes, indicating that the energy stored in the tendons depends on how much they are stretched, rather than their stiffness.

Video consigliato:

Percorso guidato

08:59

Phase Constant of a Wave Function

Displacement in Tendons

Displacement refers to the amount by which a tendon is stretched from its natural length. In this scenario, sprinters' tendons stretch 41 mm while nonathletes' tendons stretch 33 mm. The difference in displacement directly affects the amount of elastic potential energy stored, making it a key factor in calculating the energy differences between the two groups.

Video consigliato:

Percorso guidato

06:13

Displacement vs. Distance

Pratica correlata

Domanda del libro di testo

In FIGURE EX10.26, What minimum speed does a 100 g particle need at point B to reach point A?

634

views

Domanda del libro di testo

As a 15,000 kg jet plane lands on an aircraft carrier, its tail hook snags a cable to slow it down. The cable is attached to a spring with spring constant 60,000 N/m. If the spring stretches 30 m to stop the plane, what was the plane's landing speed?

1598

views

Domanda del libro di testo

FIGURE EX10.24 is the potential-energy diagram for a 500 g particle that is released from rest at A. What are the particle's speeds at B, C, and D?

2344

views

Domanda del libro di testo

In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. Suppose the dam is 80% efficient at converting the water's potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 50 MW of electricity? This is a typical value for a small hydroelectric dam.

2331

views

Domanda del libro di testo

FIGURE EX10.25 is the potential-energy diagram for a 20 g particle that is released from rest at x = 1.0 m. What is the particle's maximum speed? At what position does it have this speed?

2955

views

Domanda del libro di testo

A stretched spring stores 2.0 J of energy. How much energy will be stored if the spring is stretched three times as far?

1446

views