A slingshot will shoot a 1010-g pebble 22.022.0 m straight up. How much potential energy is stored in the slingshot's rubber band?

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

Tutti i libri di testo

Young & Freedman Calc 14th Edition

Ch 07: Potential Energy & Conservation

Problema 18a

Capitolo 7, Problema 18a

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?

Guida verificata passo dopo passo

Step 1: Identify the key variables in the problem. The mass of the pebble is 10 g (convert to kilograms: 0.010 kg), the height it reaches is 22.0 m, and we are solving for the potential energy stored in the slingshot's rubber band.

Step 2: Recall the formula for gravitational potential energy, which is given by $ U = m g h $, where $ m $ is the mass, $ g $ is the acceleration due to gravity (approximately $ 9.8 \ \text{m/s}^2 $), and $ h $ is the height.

Step 3: Substitute the known values into the formula. Use $ m = 0.010 \ \text{kg} $, $ g = 9.8 \ \text{m/s}^2 $, and $ h = 22.0 \ \text{m} $. The equation becomes $ U = (0.010)(9.8)(22.0) $.

Step 4: Understand that the potential energy stored in the slingshot's rubber band is equal to the gravitational potential energy of the pebble at its maximum height, assuming no energy is lost to air resistance or other factors.

Step 5: Perform the multiplication to calculate $ U $, but do not provide the numerical result here. The final value of $ U $ will represent the potential energy stored in the slingshot's rubber band.

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 (PE) is the energy an object possesses due to its position in a gravitational field. It is calculated using the formula PE = mgh, where m is the mass of the object, 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 case, the height is the maximum height the pebble reaches, which is 22.0 m.

Video consigliato:

Percorso guidato

06:35

Gravitational Potential Energy

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In the context of the slingshot, the elastic potential energy stored in the rubber band is converted into gravitational potential energy as the pebble is launched upward. This principle helps in understanding how the energy stored in the slingshot translates into the energy of the pebble at its peak height.

Video consigliato:

Percorso guidato

06:24

Conservation Of Mechanical Energy

Elastic Potential Energy

Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing. For a slingshot, this energy is stored in the rubber band when it is pulled back. The amount of elastic potential energy can be calculated using the formula PE_elastic = 1/2 kx², where k is the spring constant and x is the displacement from the equilibrium position. This energy is what propels the pebble when the slingshot is released.

Video consigliato:

Percorso guidato

07:24

Potential Energy Graphs

Pratica correlata

Domanda del libro di testo

A slingshot will shoot a $10$ -g pebble $22.0$ m straight up. With the same potential energy stored in the rubber band, how high can the slingshot shoot a $25$ -g pebble? What physical effects did you ignore in solving this problem?

2123

views

Domanda del libro di testo

A spring of negligible mass has force constant $k = 1600$ N/m. How far must the spring be compressed for $3.20$ J of potential energy to be stored in it?

1620

views

Domanda del libro di testo

A spring of negligible mass has force constant $k equals 800$ N/m. How far must the spring be compressed for $1.20$ J of potential energy to be stored in it?

2811

views

rank

Domanda del libro di testo

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?

1389

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