Ch 07: Potential Energy & Conservation

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo

Young & Freedman Calc 14th Edition

Ch 07: Potential Energy & Conservation

Problema 1a

Capitolo 7, Problema 1a

In one day, a $75$ -kg mountain climber ascends from the $1500$ -m level on a vertical cliff to the top at $2400$ m. The next day, she descends from the top to the base of the cliff, which is at an elevation of $1350$ m. What is her change in gravitational potential energy on the first day?

Guida verificata passo dopo passo

Step 1: Recall the formula for gravitational potential energy, which is given by:

U = m g h

, where

U

is the gravitational potential energy,

m

is the mass of the object,

g

is the acceleration due to gravity (approximately 9.8 m/s²), and

h

is the height above a reference point.

Step 2: Calculate the change in gravitational potential energy for the first day. The change in gravitational potential energy is given by:

ΔU = m g (h

_f - h_i), where

h

_f is the final height and

h

_i is the initial height.

Step 3: Substitute the given values into the formula. The mass of the climber is

75

kg, the acceleration due to gravity is

9.8

m/s², the initial height is

1500

m, and the final height is

2400

Step 4: Perform the subtraction for the height difference:

h

_f - h_i = 2400 - 1500 m. This gives the height difference.

Step 5: Multiply the mass, acceleration due to gravity, and the height difference to find the change in gravitational potential energy:

ΔU = 75 × 9.8 × (2400 - 1500)

. This will give the change in gravitational potential energy for the first day.

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.

Gravitational Potential Energy

Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field. It is calculated using the formula GPE = mgh, where m is mass, g is the acceleration due to gravity (approximately 9.81 m/s² on Earth), and h is the height above a reference point. In this scenario, the climber's change in height directly affects her GPE.

Video consigliato:

Percorso guidato

06:35

Gravitational Potential Energy

Change in Height

The change in height is a critical factor in determining the change in gravitational potential energy. It is calculated by subtracting the initial height from the final height. In the given problem, the climber ascends from 1500 m to 2400 m, resulting in a height change of 900 m, which is essential for calculating the GPE change.

Video consigliato:

Percorso guidato

06:50

Specific Heat & Temperature Changes

Mass and Weight

Mass is a measure of the amount of matter in an object, typically measured in kilograms. Weight, on the other hand, is the force exerted by gravity on that mass, calculated as weight = mass × gravity. In this problem, the climber's mass of 75 kg is used to determine the gravitational potential energy change as she ascends the cliff.

Video consigliato:

Percorso guidato

10:19

Torque Due to Weight

Pratica correlata

Domanda del libro di testo

A slingshot will shoot a $10$ -g pebble $22.0$ m straight up. How much potential energy is stored in the slingshot's rubber band?

2512

views

Domanda del libro di testo

Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length $20$ m that makes an angle of $45 degrees$ with the vertical, steps off his tree limb, and swings down and then up to Jane's open arms. When he arrives, his vine makes an angle of $30 degrees$ with the vertical. Determine whether he gives her a tender embrace or knocks her off her limb by calculating Tarzan's speed just before he reaches Jane. Ignore air resistance and the mass of the vine.

3006

views

rank

Domanda del libro di testo

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?

3943

views

rank

In one day, a 7575-kg mountain climber ascends from the 15001500-m level on a vertical cliff to the top at 24002400 m. The next day, she descends from the top to the base of the cliff, which is at an elevation of 13501350 m. What is her change in gravitational potential energy on the first day?

Risposta video verificata per un problema simile:

Concetti chiave

Gravitational Potential Energy

Change in Height

Mass and Weight

In one day, a $75$ -kg mountain climber ascends from the $1500$ -m level on a vertical cliff to the top at $2400$ m. The next day, she descends from the top to the base of the cliff, which is at an elevation of $1350$ m. What is her change in gravitational potential energy on the first day?